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ABC of multi-fractal spacetimes and fractional sea turtles: We clarify what it means to have a spacetime fractal geometry in quantum
gravity and show that its properties differ from those of usual fractals. A
weak and a strong definition of multi-scale and multi-fractal spacetimes are
given together with a sketch of the landscape of multi-scale theories of
gravitation. Then, in the context of the fractional theory with
$q$-derivatives, we explore the consequences of living in a multi-fractal
spacetime. To illustrate the behavior of a non-relativistic body, we take the
entertaining example of a sea turtle. We show that, when only the time
direction is fractal, sea turtles swim at a faster speed than in an ordinary
world, while they swim at a slower speed if only the spatial directions are
fractal. The latter type of geometry is the one most commonly found in quantum
gravity. For time-like fractals, relativistic objects can exceed the speed of
light, but strongly so only if their size is smaller than the range of
particle-physics interactions. We also find new results about log-oscillating
measures, the measure presentation and their role in physical observations and
in future extensions to nowhere-differentiable stochastic spacetimes. | Tachyon Condensation in Large Magnetic Fields with Background
Independent String Field Theory: We discuss the problem of tachyon condensation in the framework of background
independent open string field theory. We show, in particular, that the
computation of the string field theory action simplifies considerably if one
looks at closed string backgrounds with a large B field, and can be carried out
exactly for a generic tachyon profile. We confirm previous results on the form
of the exact tachyon potential, and we find, within this framework, solitonic
solutions which correspond to lower dimensional unstable branes. |
The Renormalization Group and the Effective Action: The renormalization group is used to sum the leading-log (LL) contributions
to the effective action for a large constant external gauge field in terms of
the one-loop renormalization group (RG) function beta, the next-to-leading-log
(NLL) contributions in terms of the two-loop RG function etc. The log
independent pieces are not determined by the RG equation, but can be fixed by
the anomaly in the trace of the energy-momentum tensor. Similar considerations
can be applied to the effective potential V for a scalar field phi; here the
log independent pieces are fixed by the condition V'(phi=v)=0. | Notes on instantons in topological field theory and beyond: This is a brief summary of our studies of quantum field theories in a special
limit in which the instantons are present, the anti-instantons are absent, and
the perturbative corrections are reduced to one-loop. We analyze the
corresponding models as full-fledged quantum field theories, beyond their
topological sector. We show that the correlation functions of all, not only
topological (or BPS), observables may be studied explicitly in these models,
and the spectrum may be computed exactly. An interesting feature is that the
Hamiltonian is not always diagonalizable, but may have Jordan blocks, which
leads to the appearance of logarithms in the correlation functions. We also
find that in the models defined on Kahler manifolds the space of states
exhibits holomorphic factorization. In particular, in dimensions two and four
our theories are logarithmic conformal field theories. |
Factorization of Chiral String Amplitudes: We re-examine a closed-string model defined by altering the boundary
conditions for one handedness of two-dimensional propagators in
otherwise-standard string theory. We evaluate the amplitudes using
Kawai-Lewellen-Tye factorization into open-string amplitudes. The only
modification to standard string theory is effectively that the spacetime
Minkowski metric changes overall sign in one open-string factor. This cancels
all but a finite number of states: As found in earlier approaches, with enough
supersymmetry (e.g., type II) the tree amplitudes reproduce those of the
massless truncation of ordinary string theory. However, we now find for the
other cases that additional fields, formerly thought to be auxiliary, describe
new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic).
The tachyon is always a ghost, but can be avoided in the heterotic case. | Nonlinear Hydrodynamics from Flow of Retarded Green's Function: We study the radial flow of retarded Green's function of energy-momentum
tensor and $R$-current of dual gauge theory in presence of generic higher
derivative terms in bulk Lagrangian. These are first order non-linear Riccati
equations. We solve these flow equations analytically and obtain second order
transport coefficients of boundary plasma. This way of computing transport
coefficients has an advantage over usual Kubo approach. The non-linear equation
turns out to be a linear first order equation when we study the Green's
function perturbatively in momentum. We consider several examples including
$Weyl^4$ term and generic four derivative terms in bulk. We also study the flow
equations for $R$-charged black holes and obtain exact expressions for second
order transport coefficients for dual plasma in presence of arbitrary chemical
potentials. Finally we obtain higher derivative corrections to second order
transport coefficients of boundary theory dual to five dimensional gauge
supergravity. |
Spectrum continuity and level repulsion: the Ising CFT from
infinitesimal to finite $\boldsymbol\varepsilon$: Using numerical conformal bootstrap technology we perform a non-perturbative
study of the Ising CFT and its spectrum from infinitesimal to finite values of
$\varepsilon=4-d$. Exploiting the recent navigator bootstrap method in
conjunction with the extremal functional method, we test various qualitative
and quantitative features of the $\varepsilon$-expansion. We follow the scaling
dimensions of numerous operators from the perturbatively controlled regime to
finite coupling. We do this for $\mathbb Z_2$-even operators up to spin 12 and
for $\mathbb Z_2$-odd operators up to spin 6 and find a good matching with
perturbation theory. In the finite coupling regime we observe two operators
whose dimensions approach each other and then repel, a phenomenon known as
level repulsion and which can be analyzed via operator mixing. Our work
improves on previous studies in both increased precision and the number of
operators studied, and is the first to observe level repulsion in the conformal
bootstrap. | PP-waves from Nonlocal Theories: We study the Penrose limit of ODp theory. There are two different PP-wave
limits of the theory. One of them is a ten dimensional PP-wave and the other a
four dimensional one. We observe the later one leads to an exactly solvable
background for type II string theories where we have both NS and RR fields. The
Penrose limit of different branes of string (M-theory) in a nonzero B/E field
(C field) is also studied. These backgrounds are conjectured to provide dual
description of NCSYM, NCOS and OM theory. We see that under S-duality the
subsector of NCSYM$_4$ and NCOS$_4$ which are dual to the corresponding string
theory on PP-wave coming from NCYM$_4$ and NCOS$_4$ map to each other for given
null geodesic. |
Large N Field Theories, String Theory and Gravity: We review the holographic correspondence between field theories and string/M
theory, focusing on the relation between compactifications of string/M theory
on Anti-de Sitter spaces and conformal field theories. We review the background
for this correspondence and discuss its motivations and the evidence for its
correctness. We describe the main results that have been derived from the
correspondence in the regime that the field theory is approximated by classical
or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge
theory in four dimensions, but we discuss also field theories in other
dimensions, conformal and non-conformal, with or without supersymmetry, and in
particular the relation to QCD. We also discuss some implications for black
hole physics. | On the SLq(2) extension of the standard model and the measure of charge: Our SLq(2) extension of the standard model is constructed by replacing the
elementary field operators, $\Psi (x)$, of the standard model by
$\hat{\Psi}^{j}_{mm'}(x) D^{j}_{mm'}$ where $D^{j}_{mm'}$ is an element of the
$2j + 1$ dimensional representation of the SLq(2) algebra, which is also the
knot algebra. The allowed quantum states $(j,m,m')$ are restricted by the
topological conditions \begin{equation*} (j,m,m') = \frac{1}{2}(N,w,r+o)
\end{equation*} postulated between the states of the quantum knot $(j,m,m')$
and the corresponding classical knot $(N,w,r+o)$ where the $(N,w,r)$ are (the
number of crossings, the writhe, the rotation) of the 2d projection of the
corresponding oriented classical knot. Here $o$ is an odd number that is
required by the difference in parity between $w$ and $r$. There is also the
empirical restriction on the allowed states \begin{equation*}
(j,m,m')=3(t,-t_3,-t_0)_L \end{equation*} that holds at the $j=\frac{3}{2}$
level, connecting quantum trefoils $(\frac{3}{2},m,m')$ with leptons and quarks
$(\frac{1}{2}, -t_3, -t_0)_L$. The so constructed knotted leptons and quarks
turn out to be composed of three $j=\frac{1}{2}$ particles which unexpectedly
agree with the preon models of Harrari and Shupe. The $j=0$ particles, being
electroweak neutral, are dark and plausibly greatly outnumber the quarks and
leptons. The SLq(2) or $(j,m,m')$ measure of charge has a direct physical
interpretation since $2j$ is the total number of preonic charges while $2m$ and
$2m'$ are the numbers of writhe and rotation sources of preonic charge. The
total SLq(2) charge of a particle, measured by writhe and rotation and composed
of preons, sums the signs of the counterclockwise turns $(+1)$ and clockwise
turns $(-1)$ that any energy-momentum current makes in going once around the
knot...
Keywords: Quantum group; electroweak; knot models; preon models; dark matter. |
TeV scale 5D $SU(3)_W$ unification and the fixed point anomaly
cancellation with chiral split multiplets: A possibility of 5D gauge unification of $SU(2)_L \times U(1)_Y$ in $SU(3)_W$
is examined. The orbifold compactification allows fixed points where
$SU(2)_L\times U(1)_Y$ representations can be assigned. We present a few
possibilities which give long proton lifetime, top-bottom mass hierarchy from
geometry, and reasonable neutrino masses. In general, these {\it chiral models}
can lead to fixed point anomalies. We can show easily, due to the simplicity of
the model, that these anomalies are cancelled by the relevant Chern-Simons
terms for all the models we consider. It is also shown that the fixed point
U(1)--graviton--graviton anomaly cancels without the help from the Chern-Simons
term. Hence, we conjecture that the fixed point anomalies can be cancelled if
the effective 4D theory is made anomaly free by locating chiral fermions at the
fixed points. | Deep inelastic scattering off scalar mesons in the 1/N expansion from
the D3D7-brane system: Deep inelastic scattering (DIS) of charged leptons off scalar mesons in the
$1/N$ expansion is studied by using the gauge/gravity duality. We focus on the
D3D7-brane system and investigate the corresponding structure functions by
considering both the high energy limit and the $1/N$ expansion. These limits do
not commute. From the D7-brane DBI action we derive a Lagrangian at sub-leading
order in the D7-brane fluctuations and obtain a number of interactions some of
which become relevant for two-hadron final-state DIS. By considering first the
high energy limit followed by the large $N$ one, our results fit lattice QCD
data within $1.27\%$ for the first three moments of $F_2$ for the lightest
pseudoscalar meson. |
Tachyon Condensation, Boundary State and Noncommutative Solitons: We discuss the tachyon condensation in a single unstable D-brane in the
framework of boundary state formulation. The boundary state in the background
of the tachyon condensation and the NS B-field is explicitly constructed. We
show in both commutative theory and noncommutative theory that the unstable
D-branes behaves like an extended object and eventually reduces to the lower
dimensional D-branes as the system approaches the infrared fixed point. We
clarify the relationship between the commutative field theoretical description
of the tachyon condensation and the noncommutative one. | Remarks on A-branes, Mirror Symmetry, and the Fukaya category: We discuss D-branes of the topological A-model (A-branes), which are believed
to be closely related to the Fukaya category. We give string theory arguments
which show that A-branes are not necessarily Lagrangian submanifolds in the
Calabi-Yau: more general coisotropic branes are also allowed, if the line
bundle on the brane is not flat. We show that a coisotropic A-brane has a
natural structure of a foliated manifold with a transverse holomorphic
structure. We argue that the Fukaya category must be enlarged with such objects
for the Homological Mirror Symmetry conjecture to be true. |
Killing symmetries of generalized Minkowski spaces. 3-Space-time
translations in four dimensions: In this paper, we continue the study of the Killing symmetries of a
N-dimensional generalized Minkowski space, i.e. a space endowed with a (in
general non-diagonal) metric tensor, whose coefficients do depend on a set of
non-metrical coodinates. We discuss here the translations in such spaces, by
confining ourselves (without loss of generality) to the four-dimensional case.
In particular, the results obtained are specialized to the case of a
''deformed'' Minkowski space $\widetilde{M_{4}}$ (i.e. a pseudoeuclidean space
with metric coefficients depending on energy). | A note on brane boxes at finite string coupling: We consider N=1 supersymmetric SU(N_c) gauge theories, using the type IIB
brane construction recently proposed by Hanany and Zaffaroni. At non-zero
string coupling, we find that the bending of branes imposes consistency
conditions that allow only non-anomalous gauge theories with stable vacua,
i.e., N_f >= N_c, to be constructed. We find qualitative differences between
the brane configurations for N_f <= 3N_c and N_f > 3N_c, corresponding to
asymptotically free and infrared free theories respectively. We also discuss
some properties of the brane configurations that may be relevant to
constructing Seiberg's duality in this framework. |
Can Magnetic Charge and Quantum Mechanics Co-exist ?: It is proven that if more than a single magnetic charge exists it is
impossible to define a proper quantum mechanical angular momentum operator for
an electrically charged particle in the field of the magnetic charges. Assuming
that quantum mechanics is correct we conclude that free magnetic charges (i.e.
magnetic charges with a Coulomb-like magnetic field) can not exist. The only
apparent way to avoid this conclusion is if magnetic charges do exist, they
must be permanently confined in monopole anti-monopole pairs, much in the same
way quarks are thought to be confined. | Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge
theory on D4-brane and an effective curvature: The U(1) gauge dynamics on a D4-brane is revisited, with a two form, to
construct an effective curvature theory in a second order formalism. We exploit
the local degrees in a two form, and modify its dynamics in a gauge invariant
way, to incorporate a non-perturbative metric fluctuation in an effective
D4-brane. Interestingly, the near horizon D4-brane is shown to describe an
asymptotic Anti de Sitter (AdS) in a semi-classical regime. Using Weyl
scaling(s), we obtain the emergent rotating geometries leading to primordial de
Sitter (dS) and AdS vacua in a quantum regime. Under a discrete transformation,
we re-arrange the mixed dS patches to describe a Schwazschild-like dS (SdS) and
a topological-like dS (TdS) black holes. We analyze SdS vacuum for Hawking
radiations to arrive at Nariai geometry, where a discrete torsion forms a
condensate. We perform thermal analysis to identify Nariai vacuum with a TdS.
Investigation reveals an AdS patch within a thermal dS brane, which may provide
a clue to unfold dS/CFT. In addition, the role of dark energy, sourced by a
discrete torsion, in the dS vacua is investigated using Painleve geometries. It
is argued that a D-instanton pair is created by a discrete torsion, with a Big
Bang/Crunch, at the past horizon in a pure dS. Nucleation, of brane/anti-brane
pair(s), is qualitatively analyzed to construct an effective space-time on a
D4-brane and its anti brane. Analysis re-assures the significant role played by
a non-zero mode, of NS-NS two form, to generalize the notion of branes within a
brane. |
Exact Solution of Noncommutative U(1) Gauge Theory in 4-Dimensions: Noncommutative U(1) gauge theory on the Moyal-Weyl space ${\bf
R}^2{\times}{\bf R}^2_{\theta}$ is regularized by approximating the
noncommutative spatial slice ${\bf R}^2_{\theta}$ by a fuzzy sphere of matrix
size $L$ and radius $R$ . Classically we observe that the field theory on the
fuzzy space ${\bf R}^2{\times}{\bf S}^2_L$ reduces to the field theory on the
Moyal-Weyl plane ${\bf R}^2{\times}{\bf R}^2_{\theta}$ in the flattening
continuum planar limits $R,L{\longrightarrow}{\infty}$ where
$R^2/L^{2q}{\simeq}{\theta}^2/4^q$ and $q>{3/2}$ . The effective
noncommutativity parameter is found to be given by
${\theta}_{eff}^2{\sim}2{\theta}^2(\frac{L}{2})^{2q-1}$ and thus it corresponds
to a strongly noncommuting space. In the quantum theory it turns out that this
prescription is also equivalent to a dimensional reduction of the model where
the noncommutative U(1) gauge theory in 4 dimensions is shown to be equivalent
in the large $L$ limit to an ordinary $O(M)$ non-linear sigma model in 2
dimensions where $M{\sim}3L^2$ . The Moyal-Weyl model defined this way is also
seen to be an ordinary renormalizable theory which can be solved exactly using
the method of steepest descents . More precisely we find for a fixed
renormalization scale $\mu$ and a fixed renormalized coupling constant $g_r^2$
an $O(M)-$symmetric mass, for the different components of the sigma field,
which is non-zero for all values of $g_r^2$ and hence the $O(M)$ symmetry is
never broken in this solution . We obtain also an exact representation of the
beta function of the theory which agrees with the known one-loop perturbative
result . | Normal ordering and boundary conditions for fermionic string coordinates: We build up normal ordered products for fermionic open string coordinates
consistent with boundary conditions. The results are obtained considering the
presence of antisymmetric tensor fields. We find a discontinuity of the normal
ordered products at string endpoints even in the absence of the background. We
discuss how the energy momentum tensor also changes at the world-sheet boundary
in such a way that the central charge keeps the standard value at string end
points. |
$Ω$ versus Graviphoton: I study the deformation of the topological string by $\bar\Omega$, the
complex conjugate of the $\Omega$-deformation. Namely, I identify $\bar\Omega$
in terms of a physical state in the string spectrum and verify that the
deformed Yang-Mills and ADHM actions are reproduced. This completes the study
initiated recently [1] where we show that $\bar\Omega$ decouples from the
one-loop topological amplitudes in heterotic string theory. Similarly to the
N=2* deformation, I show that the quadratic terms in the effective action play
a crucial role in obtaining the correct realisation of the full
$\Omega$-deformation. Finally, I comment on the differences between the
graviphoton and the $\Omega$-deformation in general and discuss possible
$\bar\Omega$ remnants at the boundary of the string moduli space. | Off-Shell Duality in Maxwell and Born-Infeld Theories: It is well known that the classical equations of motion of Maxwell and
Born-Infeld theories are invariant under a duality symmetry acting on the field
strengths. We review the implementation of the SL(2,Z) duality in these
theories as linear but non-local transformations of the potentials. |
Conformal Invariance of the One-Loop All-Plus Helicity Scattering
Amplitudes: The massless QCD Lagrangian is conformally invariant and, as a consequence,
so are the tree-level scattering amplitudes. However, the implications of this
powerful symmetry at loop level are only beginning to be explored
systematically. Even for finite loop amplitudes, the way conformal symmetry
manifests itself may be subtle, e.g. in the form of anomalous conformal Ward
identities. As they are finite and rational, the one-loop all-plus and
single-minus amplitudes are a natural first step towards understanding the
conformal properties of Yang-Mills theory at loop level. Remarkably, we find
that the one-loop all-plus amplitudes are conformally invariant, whereas the
single-minus are not. Moreover, we present a formula for the one-loop all-plus
amplitudes where the symmetry is manifest term by term. Surprisingly, each term
transforms covariantly under directional dual conformal variations. We prove
the formula directly using recursive techniques, and check that it has the
correct physical factorisations. | A Critical Cosmological Constant from Millimeter Extra Dimensions: We consider `brane universe' scenarios with standard-model fields localized
on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is
rotationally symmetric about the brane, local quantities in the bulk are
insensitive to the couplings on the brane. This potentially allows
compactifications where the effective 4-dimensional cosmological constant is
independent of the couplings on the 3-brane. We consider several possible
singularity-free compactification mechanisms, and find that they do not
maintain this property. We also find solutions with naked spacetime
singularities, and we speculate that new short-distance physics can become
important near the singularities and allow a compactification with the desired
properties. The picture that emerges is that standard-model loop contributions
to the effective 4-dimensional cosmological constant can be cut off at
distances shorter than the compactification scale. At shorter distance scales,
renormalization effects due to standard-model fields renormalize the 3-brane
tension, which changes a deficit angle in the transverse space without
affecting local quantities in the bulk. For a compactification scale of order
10^{-2} mm, this gives a standard-model contribution to the cosmological
constant in the range favored by cosmology. |
Multi-Stream Inflation in a Landscape: There are hidden observables for inflation, such as features localized in
position space, which do not manifest themselves when only one inflation
trajectory is considered. To address this issue, we investigate inflation
dynamics in a landscape mimicked by a random potential. We calculate the
probability for bifurcation of the inflation trajectory in multi-stream
inflation. Depending on the shape of the random bumps and the distance between
bumps in the potential, there is a phase transition: on one side of the
critical curve in parameter space isocurvature fluctuation are exponentially
amplified and bifurcation becomes very probable. On the other side bifurcation
is dominated by a random walk where bifurcations are less likely to happen. | Integrable Renormalization I: the Ladder Case: In recent years a Hopf algebraic structure underlying the process of
renormalization in quantum field theory was found. It led to a Birkhoff
factorization for (regularized) Hopf algebra characters, i.e. for Feynman
rules. In this work we would like to show that this Birkhoff factorization
finds its natural formulation in terms of a classical r-matrix, coming from a
Rota-Baxter structure underlying the target space of the regularized Hopf
algebra characters. Working in the rooted tree Hopf algebra, the simple case of
the Hopf subalgebra of ladder trees is treated in detail. The extension to the
general case, i.e. the full Hopf algebra of rooted trees or Feynman graphs is
briefly outlined. |
Semi-classical BMS-blocks from the Oscillator Construction: Flat-space holography requires a thorough understanding of BMS symmetry. We
introduce an oscillator construction of the highest-weight representation of
the $\mathfrak{bms}_3$ algebra and show that it is consistent with known
results concerning the $\mathfrak{bms}_3$ module. We take advantage of this
framework to prove that $\mathfrak{bms}_3$-blocks exponentiate in the
semi-classical limit, where one of the central charges is large. Within this
context, we compute perturbatively heavy, and heavy-light vacuum
$\mathfrak{bms}_3$-blocks. | PP-waves from rotating and continuously distributed D3-branes: We study families of PP-wave solutions of type-IIB supergravity that have
(light-cone) time dependent metrics and RR five-form fluxes. They arise as
Penrose limits of supergravity solutions that correspond to rotating or
continuous distributions of D3-branes. In general, the solutions preserve
sixteen supersymmetries. On the dual field theory side these backgrounds
describe the BMN limit of N=4 SYM when some scalars in the field theory have
non-vanishing expectation values. We study the perturbative string spectrum and
in several cases we are able to determine it exactly for the bosons as well as
for the fermions. We find that there are special states for particular values
of the light-cone constant P_+. |
Quantum Field Theory without Infinite Renormalization: Although Quantum field theory has been very successful in explaining
experiment, there are two aspects of the theory that remain quite troubling.
One is the no-interaction result proved in Haag's theorem. The other is the
existence of infinite perturbation expansion terms that need to be absorbed
into theoretically unknown but experimentally measurable quantities like charge
and mass -- i.e. renormalization. Here it will be shown that the two problems
may be related. A "natural" method of eliminating the renormalization problem
also sidesteps Haag's theorem automatically. Existing renormalization schemes
can at best be considered a temporary fix as perturbation theory assumes
expansion terms to be "small" -- and infinite terms are definitely not so (even
if they are renormalized away). String theories may be expected to help the
situation because the infinities can be traced to the point-nature of
particles. However, string theories have their own problems arising from the
extra space dimensions required. Here a more directly physical remedy is
suggested. Particles are modeled as extended objects (like strings). But,
unlike strings, they are composites of a finite number of constituents each of
which resides in the normal 4-dimensional space-time. The constituents are
bound together by a manifestly covariant confining potential. This approach no
longer requires infinite renormalizations. At the same time it sidesteps the
no-interaction result proved in Haag's theorem. | Conformal supergravity in three dimensions: Off-shell actions: Using the off-shell formulation for N-extended conformal supergravity in
three dimensions, which has recently been presented in arXiv:1305.3132, we
construct superspace actions for conformal supergravity theories with N<6. For
each of the cases considered, we work out the complete component action as well
as the gauge transformation laws of the fields belonging to the Weyl
supermultiplet. The N=1 and N=2 component actions derived coincide with those
proposed by van Nieuwenhuizen and Rocek in the mid-1980s. The off-shell N=3,
N=4 and N=5 supergravity actions are new results. Upon elimination of the
auxiliary fields, these actions reduce to those constructed by Lindstrom and
Rocek in 1989 (and also by Gates and Nishino in 1993). |
Exercises in equivariant cohomology: Equivariant cohomology is a mathematical framework particularly well adapted
to a kinematical understanding of topological gauge theories of the
cohomological type. It also sheds some light on gauge fixing, a necessary field
theory operation connected with the non compactness of the gauge group. The
respective roles of fields and observables are emphasized throughout. | Signatures of Initial State Modifications on Bispectrum Statistics: Modifications of the initial-state of the inflaton field can induce a
departure from Gaussianity and leave a testable imprint on the higher order
correlations of the CMB and large scale structures in the Universe. We focus on
the bispectrum statistics of the primordial curvature perturbation and its
projection on the CMB. For a canonical single-field action the three-point
correlator enhancement is localized, maximizing in the collinear limit,
corresponding to enfolded or squashed triangles in comoving momentum space. We
show that the available local and equilateral template are very insensitive to
this localized enhancement and do not generate noteworthy constraints on
initial-state modifications. On the other hand, when considering the addition
of a dimension 8 higher order derivative term, we find a dominant rapidly
oscillating contribution, which had previously been overlooked and whose
significantly enhanced amplitude is independent of the triangle under
consideration. Nevertheless, the oscillatory nature of (the sign of) the
correlation function implies the signal is nearly orthogonal to currently
available observational templates, strongly reducing the sensitivity to the
enhancement. Constraints on departures from the standard Bunch-Davies vacuum
state can be derived, but also depend on the next-to-leading terms. We
emphasize that the construction and application of especially adapted templates
could lead to CMB bispectrum constraints on modified initial states already
competing with those derived from the power spectrum. |
Knot solitons in modified Ginzburg-Landau model: We study a modified version of the Ginzburg-Landau model suggested by Ward
and show that Hopfions exist in it as stable static solutions, for values of
the Hopf invariant up to at least 7. We also find that their properties closely
follow those of their counterparts in the Faddeev-Skyrme model. Finally, we
lend support to Babaev's conjecture that longer core lengths yield more stable
solitons and propose a possible mechanism for constructing Hopfions in pure
Ginzburg-Landau model. | Temporal vs Spatial Conservation and Memory Effect in Electrodynamics: We consider the standard Maxwell's theory in 1+3 dimensions in the presence
of a timelike boundary. In this context, we show that (generalized)
Ampere-Maxwell's charge appears as a Noether charge associated with the Maxwell
U(1) gauge symmetry which satisfies a spatial conservation equation.
Furthermore, we also introduce the notion of spatial memory field and its
corresponding memory effect. Finally, similar to the temporal case through the
lens of Strominger's triangle proposal, we show how spatial memory and
conservation are related. |
Degrees of freedom of massless boson and fermion fields in any even
dimension: This is a discussion on degrees of freedom of massless fermion and boson
fields, if they are free or weakly interacting. We generalize the gauge fields
of $S^{ab}$ - $\omega_{abc}$ - and of $\tilde{S}^{ab}$ - $
\tilde{\omega}_{abc}$ - of the spin-charge-family to the gauge fields of all
possible products of $\gamma^a$'s and of all possible products of
$\tilde{\gamma}^a$'s, the first taking care in the {\it spin-charge-family}
theory of the spins and charges quantum numbers ($\tau^{Ai}=\sum_{a,b}
c^{Ai}{}_{ab} \,S^{ab}$) of fermions, the second ($\tilde{\tau}^{Ai}=
\sum_{a,b} \tilde{c}^{Ai}{}_{ab}\, \tilde{S}^{ab}$) taking care of the families
quantum numbers. | Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and
Central Functions: We consider N=1 supersymmetric gauge theories in which the couplings are
allowed to be space-time dependent functions. Both the gauge and the
superpotential couplings become chiral superfields. As has recently been shown,
a new topological anomaly appears in models with space-time dependent gauge
coupling. Here we show how this anomaly may be used to derive the NSVZ beta
function in a particular, well-determined renormalisation scheme, both without
and with chiral matter. Moreover we extend the topological anomaly analysis to
theories coupled to a classical curved superspace background, and use it to
derive an all-order expression for the central charge c, the coefficient of the
Weyl tensor squared contribution to the conformal anomaly. We also comment on
the implications of our results for the central charge a expected to be of
relevance for a four-dimensional C-theorem. |
Polyakov-Mellin Bootstrap for AdS loops: We consider holographic CFTs and study their large $N$ expansion. We use
Polyakov-Mellin bootstrap to extract the CFT data of all operators, including
scalars, till $O(1/N^4)$. We add a contact term in Mellin space, which
corresponds to an effective $\phi^4$ theory in AdS and leads to anomalous
dimensions for scalars at $O(1/N^2)$. Using this we fix $O(1/N^4)$ anomalous
dimensions for double trace operators finding perfect agreement with
\cite{loopal} (for $\Delta_{\phi}=2$). Our approach generalizes this to any
dimensions and any value of conformal dimensions of external scalar field. In
the second part of the paper, we compute the loop amplitude in AdS which
corresponds to non-planar correlators of in CFT. More precisely, using CFT data
at $O(1/N^4)$ we fix the AdS bubble diagram and the triangle diagram for the
general case. | Non-Perturbative Solution of Matrix Models Modified by Trace-Squared
Terms: We present a non-perturbative solution of large $N$ matrix models modified by
terms of the form $ g(\Tr\Phi^4)^2$, which add microscopic wormholes to the
random surface geometry. For $g<g_t$ the sum over surfaces is in the same
universality class as the $g=0$ theory, and the string susceptibility exponent
is reproduced by the conventional Liouville interaction $\sim e^{\alpha_+
\phi}$. For $g=g_t$ we find a different universality class, and the string
susceptibility exponent agrees for any genus with Liouville theory where the
interaction term is dressed by the other branch, $e^{\alpha_- \phi}$. This
allows us to define a double-scaling limit of the $g=g_t$ theory. We also
consider matrix models modified by terms of the form $g O^2$, where $O$ is a
scaling operator. A fine-tuning of $g$ produces a change in this operator's
gravitational dimension which is, again, in accord with the change in the
branch of the Liouville dressing. |
Quantum Trilogy: Discrete Toda, Y-System and Chaos: We discuss a discretization of the quantum Toda field theory associated with
a semisimple finite-dimensional Lie algebra or a tamely-laced
infinite-dimensional Kac-Moody algebra $G$, generalizing the previous
construction of discrete quantum Liouville theory for the case $G=A_1$. The
model is defined on a discrete two-dimensional lattice, whose spatial direction
is of length $L$. In addition we also find a "discretized extra dimension"
whose width is given by the rank $r$ of $G$, which decompactifies in the large
$r$ limit. For the case of $G=A_N$ or $A_{N-1}^{(1)}$, we find a symmetry
exchanging $L$ and $N$ under appropriate spatial boundary conditions. The
dynamical time evolution rule of the model is a quantizations of the so-called
Y-system, and the theory can be well-described by the quantum cluster algebra.
We discuss possible implications for recent discussions of quantum chaos, and
comment on the relation with the quantum higher Teichmuller theory of type
$A_N$. | Grassmannian sigma model on a finite interval: We discuss the two-dimensional Grassmannian sigma model $\mathbb{G}_{N, M}$
on a finite interval $L$. The different boundary conditions which allow to
obtain analytical solutions by the saddle-point method in the large $N$ limit
are considered. The nontrivial phase structure of the model on the interval
similar to $\mathbb{C}P(N)$ model is found. |
Branes And Supergroups: Extending previous work that involved D3-branes ending on a fivebrane with
$\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This
construction, in case the fivebrane is of NS type, is associated to the
three-dimensional Chern-Simons theory of a supergroup U$(m|n)$ or OSp$(m|2n)$
rather than an ordinary Lie group as in the one-sided case. By $S$-duality, we
deduce a dual magnetic description of the supergroup Chern-Simons theory; a
slightly different duality, in the orthosymplectic case, leads to a strong-weak
coupling duality between certain supergroup Chern-Simons theories on
$\mathbb{R}^3$; and a further $T$-duality leads to a version of Khovanov
homology for supergroups. Some cases of these statements are known in the
literature. We analyze how these dualities act on line and surface operators. | Effective Lagrangian in de Sitter Spacetime: Scale invariant fluctuations of metric are universal feature of quantum
gravity in de Sitter spacetime. We construct an effective Lagrangian which
summarizes their implications on local physics by integrating super-horizon
metric fluctuations. It shows infrared quantum effects are local and render
fundamental couplings time dependent. We impose Lorenz invariance on the
effective Lagrangian as it is required by the principle of general covariance.
We show that such a requirement leads to unique physical predictions by fixing
the quantization ambiguities. We explain how the gauge parameter dependence of
observables is canceled. In particular the relative evolution speed of the
couplings are shown to be gauge invariant. |
Moduli Stabilization in the Heterotic/IIB Discretuum: We consider supersymmetric compactifications of type IIB and the weakly
coupled heterotic string with G resp.H-flux and gaugino condensation in a
hidden sector included. We point out that proper inclusion of the
non-perturbative effects changes the Hodge structure of the allowed fluxes in
type IIB significantly. In the heterotic theory it is known that, in contrast
to the potential read off from dimensional reduction, the effective
four-dimensional description demands for consistency a non-vanishing H^{2,1}
component if a H^{3,0} component is already present balancing the condensate.
The H^{2,1} component causes a non-Kahlerness of the underlying geometry whose
moduli space is, however, not well-understood. We show that the occurrence of
H^{2,1} might actually be avoided by using a KKLT-like two-step procedure for
moduli stabilization. Independently of the H^{2,1} issue one-loop corrections
to the gauge couplings were argued to cause a not well-controlled strong
coupling transition. This problem can be avoided as well when the effects of
world-sheet instantons are included. They will also stabilize the Kahler
modulus what was accomplished by H^{2,1} before. | Correlation Functions in Unitary Minimal Liouville Gravity and Frobenius
Manifolds: We continue to study minimal Liouville gravity (MLG) using a dual approach
based on the idea that the MLG partition function is related to the tau
function of the A_q integrable hierarchy via the resonance transformations,
which are in turn fixed by conformal selection rules. One of the main problems
in this approach is to choose the solution of the Douglas string equation that
is relevant for MLG. The appropriate solution was recently found using
connection with the Frobenius manifolds. We use this solution to investigate
three- and four-point correlators in the unitary MLG models. We find an
agreement with the results of the original approach in the region of the
parameters where both methods are applicable. In addition, we find that only
part of the selection rules can be satisfied using the resonance
transformations. The physical meaning of the nonzero correlators, which before
coupling to Liouville gravity are forbidden by the selection rules, and also
the modification of the dual formulation that takes this effect into account
remains to be found. |
Noncommutative Supersymmetric Field Theories: We discuss some properties of noncommutative supersymmetric field theories
which do not involve gauge fields. We concentrate on the renormalizability
issue of these theories. | Canonical Chern-Simons Theory and the Braid Group on a Riemann Surface: We find an explicit solution of the Schr\"odinger equation for a Chern-Simons
theory coupled to charged particles on a Riemann surface, when the coefficient
of the Chern-Simons term is a rational number (rather than an integer) and
where the total charge is zero. We find that the wave functions carry a
projective representation of the group of large gauge transformations. We also
examine the behavior of the wave function under braiding operations which
interchange particle positions. We find that the representation of both the
braiding operations and large gauge transformations involve unitary matrices
which mix the components of the wave function. The set of wave functions are
expressed in terms of appropriate Jacobi theta functions. The matrices form a
finite dimensional representation of a particular (well known to
mathematicians) version of the braid group on the Riemann surface. We find a
constraint which relates the charges of the particles, $q$, the coefficient of
the Chern-Simons term, $k$ and the genus of the manifold, $g$: $q^2(g-1)/k$
must be an integer. We discuss a duality between large gauge transformations
and braiding operations. |
Schwinger-Keldysh Diagrammatics for Primordial Perturbations: We present a systematic introduction to the diagrammatic method for practical
calculations in inflationary cosmology, based on Schwinger-Keldysh path
integral formalism. We show in particular that the diagrammatic rules can be
derived directly from a classical Lagrangian even in the presence of derivative
couplings. Furthermore, we use quasi-single-field inflation as an example to
show how this formalism, combined with the trick of mixed propagator, can
significantly simplify the calculation of some in-in correlation functions. The
resulting bispectrum includes the lighter scalar case ($m<3H/2$) that has been
previously studied, and the heavier scalar case ($m>3H/2$) that has not been
explicitly computed for this model. The latter provides a concrete example of
quantum primordial standard clocks, in which the clock signals can be
observably large. | Tensor Field Theories: Renormalization and Random Geometry: This thesis focuses on renormalization of quantum field theories. Its first
part considers three tensor models in three dimensions, a Fermionic quartic
with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon
the large-$N$ melonic expansion of tensor models. For the first model,
invariant under $U(N)^3$, we obtain the RG flow of the two melonic couplings
and the vacuum phase diagram, from a reformulation with a diagonalizable matrix
intermediate field. The discrete chiral symmetry breaks spontaneously and we
compare with the three-dimensional Gross-Neveu model. Beyond the massless
$U(N)^3$ symmetric phase, we also observe a massive phase of same symmetry and
another where the symmetry breaks into $U(N^2)\times U(N/2)\times U(N/2)$. A
matrix model invariant under $U(N)\times U(N^2)$, with close properties, is
also studied. For the other models, with symmetry groups $U(N)^3$ and $O(N)^5$,
a non-melonic coupling (the "wheel") with an optimal scaling in $N$ drives us
to a generalized melonic expansion. The kinetic terms are taken of short- and
long-range, and we analyze perturbatively, at large-$N$, the RG flows of the
sextic couplings up to four loops. Only the rank-3 model displays non-trivial
fixed points (two real Wilson-Fisher-like in the short-range case and a line of
fixed points in the other). We finally obtain the real conformal dimensions of
the primary bilinear operators. In the second part, we establish the first
results of perturbative multi-scale renormalization for a quartic scalar field
on critical Galton-Watson trees, with a long-range kinetic term. At
criticality, an emergent infinite spine provides a space of effective dimension
$4/3$ on which to compute averaged correlation fonctions. This approach
formalizes the notion of a QFT on a random geometry. We use known probabilistic
bounds on the heat-kernel on a random graph reviewed in detail. |
Chiral Reductions of the M-Algebra: We present the chiral truncation of the eleven dimensional M-algebra down to
ten and six dimensions. In ten dimensions, we obtain a topological extension of
the $(1,0)$ Poincar\'e superalgebra that includes super one-form and super
five-form charges. Closed super three- and seven-forms associated with this
algebra are constructed. In six dimensions, we obtain a topological extension
of the $(2,0)$ and $(1,0)$ Poincar\'e superalgebras. The former includes a
quintet of super one-form charges, and a decuplet of super three-form charges,
while the latter includes a triplet of super three-form charges. | Symmetry breaking mechanisms of the 3BF action for the Standard Model
coupled to gravity: We study the details of the explicit and spontaneous symmetry breaking of the
constrained 3BF action representing the Standard Model coupled to
Einstein-Cartan gravity. First we discuss how each particular constraint breaks
the original symmetry of the topological 3BF action. Then we investigate the
spontaneous symmetry breaking and the Higgs mechanism for the electroweak
theory in the constrained 3BF form, in order to demonstrate that they can
indeed be performed in the framework of higher gauge theory. A formulation of
the Proca action as a constrained 3BF theory is also studied in detail. |
Spinning Hopf solitons on S^3 x R: We consider a field theory with target space being the two dimensional sphere
S^2 and defined on the space-time S^3 x R. The Lagrangean is the square of the
pull-back of the area form on S^2. It is invariant under the conformal group
SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms
of S^2. We construct an infinite number of exact soliton solutions with
non-trivial Hopf topological charges. The solutions spin with a frequency which
is bounded above by a quantity proportional to the inverse of the radius of
S^3. The construction of the solutions is made possible by an ansatz which
explores the conformal symmetry and a U(1) subgroup of the area preserving
diffeomorphism group. | Goldilocks Modes and the Three Scattering Bases: We consider massless scattering from the point of view of the position,
momentum, and celestial bases. In these three languages different properties of
physical processes become manifest or obscured. Within the soft sector, they
highlight distinct aspects of the infrared triangle: quantum field theory soft
theorems arise in the limit of vanishing energy $\omega$, memory effects are
described via shifts of fields at the boundary along the null time coordinate
$u$, and celestial symmetry algebras are realized via currents that appear at
special values of the conformal dimension $\Delta$. We focus on the subleading
soft theorems at $\Delta=1-s$ for gauge theory $(s=1)$ and gravity $(s=2)$ and
explore how to translate the infrared triangle to the celestial basis. We
resolve an existing tension between proposed overleading gauge transformations
as examined in the position basis and the `Goldstone-like' modes where we
expect celestial symmetry generators to appear. In the process we elucidate
various order-of-limits issues implicit in the celestial formalism. We then
generalize our construction to the tower of $w_{1+\infty}$ generators in
celestial CFT, which probe further subleading-in-$\omega$ soft behavior and are
related to subleading-in-$r$ vacuum transitions that measure higher multipole
moments of scatterers. In the end we see that the celestial basis is `just
right' for identifying the symmetry structure. |
Lattice supersymmetry, superfields and renormalization: We study Euclidean lattice formulations of non-gauge supersymmetric models
with up to four supercharges in various dimensions. We formulate the conditions
under which the interacting lattice theory can exactly preserve one or more
nilpotent anticommuting supersymmetries. We introduce a superfield formalism,
which allows the enumeration of all possible lattice supersymmetry invariants.
We use it to discuss the formulation of Q-exact lattice actions and their
renormalization in a general manner. In some examples, one exact supersymmetry
guarantees finiteness of the continuum limit of the lattice theory. As a
consequence, we show that the desired quantum continuum limit is obtained
without fine tuning for these models. Finally, we discuss the implications and
possible further applications of our results to the study of gauge and
non-gauge models. | Holographic Superconductors in Quasi-topological Gravity: In this paper we study (3+1) dimensional holographic superconductors in
quasi-topological gravity which is recently proposed by R. Myers {\it et.al.}.
Through both analytical and numerical analysis, we find in general the
condensation becomes harder with the increase of coupling parameters of higher
curvature terms. In particular, comparing with those in ordinary Gauss-Bonnet
gravity, we find that positive cubic corrections in quasi-topological gravity
suppress the condensation while negative cubic terms make it easier. We also
calculate the conductivity numerically for various coupling parameters. It
turns out that the universal relation of $\omega_g/T_c\simeq 8$ is unstable and
this ratio becomes larger with the increase of the coupling parameters. A brief
discussion on the condensation from the CFT side is also presented. |
Inhomogeneous Reheating Scenario with DBI fields: We discuss a new mechanism which can be responsible for the origin of the
primordial perturbation in inflationary models, the inhomogeneous DBI reheating
scenario. Light DBI fields fluctuate during inflation, and finally create the
density perturbations through modulation of the inflation decay rate. In this
note, we investigate the curvature perturbation and its non-Gaussianity from
this new mechanism. Presenting generalized expressions for them, we show that
the curvature perturbation not only depends on the particular process of decay
but is also dependent on the sound speed $c_s$ from the DBI action. More
interestingly we find that the non-Gaussianity parameter $f_{NL}$ is
independent of $c_s$. As an application we exemplify some decay processes which
give a viable and detectable non-Gaussianity. Finally we find a possible
connection between our model and the DBI-Curvaton mechanism. | Simple recipe for holographic Weyl anomaly: We propose a recipe - arguably the simplest - to compute the holographic
type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS
spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature
invariants that allows to read off easily, without any further computation, the
Weyl anomaly coefficients of the dual CFT. We tabulate the contributions from
quadratic, cubic and quartic purely algebraic curvature invariants and also
from terms involving derivatives of the curvature. We provide few examples,
where the anomaly coefficients have been obtained by other means, to illustrate
the effectiveness of our prescription. |
Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable
degenerations and enhanced gauge groups in F-theory duals: Eight-dimensional non-geometric heterotic strings with gauge algebra
$\mathfrak{e}_8\mathfrak{e}_7$ were constructed by Malmendier and Morrison as
heterotic duals of F-theory on K3 surfaces with $\Lambda^{1,1}\oplus E_8\oplus
E_7$ lattice polarization. Clingher, Malmendier and Shaska extended these
constructions to eight-dimensional non-geometric heterotic strings with gauge
algebra $\mathfrak{e}_7\mathfrak{e}_7$ as heterotic duals of F-theory on
$\Lambda^{1,1}\oplus E_7\oplus E_7$ lattice polarized K3 surfaces. In this
study, we analyze the points in the moduli of non-geometric heterotic strings
with gauge algebra $\mathfrak{e}_7\mathfrak{e}_7$, at which the non-Abelian
gauge groups on the F-theory side are maximally enhanced. The gauge groups on
the heterotic side do not allow for the perturbative interpretation at these
points. We show that these theories can be described as deformations of the
stable degenerations, as a result of coincident 7-branes on the F-theory side.
From the heterotic viewpoint, this effect corresponds to the insertion of
5-branes. These effects can be used to understand nonperturbative aspects of
nongeometric heterotic strings. Additionally, we build a family of elliptic
Calabi-Yau 3-folds by fibering elliptic K3 surfaces, which belong to the
F-theory side of the moduli of non-geometric heterotic strings with gauge
algebra $\mathfrak{e}_7\mathfrak{e}_7$, over $\mathbb{P}^1$. We find that
highly enhanced gauge symmetries arise on F-theory on the built elliptic
Calabi-Yau 3-folds. | Study of the nonlocal gauge invariant mass operator $\mathrm{Tr} \int
d^4x F_{μν} (D^2)^{-1} F_{μν}$ in the maximal Abelian gauge: The nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^{4}x
F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is investigated in Yang-Mills theories in the
maximal Abelian gauge. By means of the introduction of auxiliary fields a local
action is achieved, enabling us to use the algebraic renormalization in order
to prove the renormalizability of the resulting local model to all orders of
perturbation theory. |
Early Dark Energy in Type IIB String Theory: Early Dark Energy (EDE) is a promising model to resolve the Hubble Tension,
that, informed by Cosmic Microwave Background data, features a generalization
of the potential energy usually associated with axion-like particles. We
develop realizations of EDE in type IIB string theory with the EDE field
identified as either a $C_4$ or $C_2$ axion and with full closed string moduli
stabilization within the framework of either KKLT or the Large Volume Scenario.
We explain how to achieve a natural hierarchy between the EDE energy scale and
that of the other fields within a controlled effective field theory. We argue
that the data-driven EDE energy scale and decay constant can be achieved
without any tuning of the microscopic parameters for EDE fields that violate
the weak gravity conjecture, while for states that respect the conjecture it is
necessary to introduce a fine-tuning. This singles out as the most promising
EDE candidates, amongst several working models, the $C_2$ axions in LVS with 3
non-perturbative corrections to the superpotential generated by gaugino
condensation on D7-branes with non-zero world-volume fluxes. | Currents for Arbitrary Helicity: Using Mackey's classification of unitary representations of the Poincar\'e
group on massles states of arbitrary helicity we disprove the claim that states
with helicity |h|>=1 cannot couple to a conserved current by constructing such
a current. |
Analytic long-lived modes in charged critical plasma: Fluctuations around critical behavior of a holographic charged plasmas are
investigated by studying quasi-normal modes of the corresponding black branes
in 5D Einstein-Maxwell-Dilaton gravity. The near horizon geometry of black
branes approaches the well-known 2D charged string black hole in the critical
limit, for which a world-sheet description is available, and the corresponding
quasi-normal modes can be obtained analytically from the reflection amplitude
of the 2D black hole geometry. We find two distinct set of modes: a purely
imaginary ``decoupled'' set, directly following from the reflection amplitude,
and a ``non-decoupled'' set that was already identified in the neutral
holographic plasma in \cite{Betzios:2018kwn}. In the extremal limit, the former
set of imaginary quasi-normal modes coalesce on a branch cut starting from the
the origin, signaling breakdown of hydrodynamic approximation. We further
complete the black brane geometry with a slice of AdS near the boundary, to
allow for a holographic construction, and find another set of modes localized
in the UV. Finally, we develop an alternative WKB method to obtain the
quasi-normal modes in the critical limit and apply this method to study the
spectrum of hyperscaling-violating Lifshitz black branes. The critical limit of
the plasma we consider in this paper is in one-to-one correspondence with the
large D limit of Einstein's gravity which allows for an alternative interesting
interpretation of our findings. | On thermal molecular potential among micromolecules in charged AdS black
holes: Considering the unexpected similarity between the thermodynamic features of
charged AdS black holes and that of the van der Waals fluid system, we
calculate the number densities of black hole micromolecules and derive the
thermodynamic scalar curvature for the small and large black holes on the
co-existence curve based on the so-called Ruppeiner thermodynamic geometry. We
reveal that the microscopic feature of the small black hole perfectly matches
that of the ideal anyon gas, and that the microscopic feature of the large
black hole matches that of the ideal Bose gas. More importantly, we investigate
the issue of molecular potential among micromolecules of charged AdS black
holes, and point out explicitly that the well-known experiential Lennard-Jones
potential is a feasible candidate to describe interactions among black hole
micromolecules completely from a thermodynamic point of view. The behavior of
the interaction force induced by the Lennard-Jones potential coincides with
that of the thermodynamic scalar curvature. Both the Lennard-Jones potential
and the thermodynamic scalar curvature offer a clear and reliable picture of
microscopic structures for the small and large black holes on the co-existence
curve for charged AdS black holes. |
A note on scaling arguments in the effective average action formalism: The effective average action (EAA) is a scale dependent effective action
where a scale $k$ is introduced via an infrared regulator. The $k-$dependence
of the EAA is governed by an exact flow equation to which one associates a
boundary condition at a scale $\mu$. We show that the $\mu-$dependence of the
EAA is controlled by an equation fully analogous to the Callan-Symanzik
equation which allows to define scaling quantities straightforwardly.
Particular attention is paid to composite operators which are introduced along
with new sources. We discuss some simple solutions to the flow equation for
composite operators and comment their implications in the case of a local
potential approximation. | Form factors of descendant operators: $A^{(1)}_{L-1}$ affine Toda theory: In the framework of the free field representation we obtain exact form
factors of local operators in the two-dimensional affine Toda theories of the
$A^{(1)}_{L-1}$ series. The construction generalizes Lukyanov's well-known
construction to the case of descendant operators. Besides, we propose a free
field representation with a countable number of generators for the `stripped'
form factors, which generalizes the recent proposal for the sine/sinh-Gordon
model. As a check of the construction we compare numbers of the operators
defined by these form factors in level subspaces of the chiral sectors with the
corresponding numbers in the Lagrangian formalism. We argue that the
construction provides a correct counting for operators with both chiralities.
At last we study the properties of the operators with respect to the Weyl
group. We show that for generic values of parameters there exist Weyl invariant
analytic families of the bases in the level subspaces. |
Pure N=2 Super Yang-Mills and Exact WKB: We apply exact WKB methods to the study of the partition function of pure N=2
epsilon_i-deformed gauge theory in four dimensions in the context of the 2d/4d
correspondence. We study the partition function at leading order in
epsilon_2/epsilon_1 (i.e. at large central charge) and in an expansion in
epsilon_1. We find corrections of the form ~ exp[- SW periods / epsilon_1] to
this expansion. We attribute these to the exchange of the order of summation
over gauge instanton number and over powers of epsilon_1 when passing from the
Nekrasov form of the partition function to the topological string theory
inspired form. We conjecture that such corrections should be computable from a
worldsheet perspective on the partition function. Our results follow upon the
determination of the Stokes graphs associated to the Mathieu equation with
complex parameters and the application of exact WKB techniques to compute the
Mathieu characteristic exponent. | Teukolsky master equation and Painlevé transcendents: numerics and
extremal limit: We conduct an analysis of the quasi-normal modes for generic spin
perturbations of the Kerr black hole using the isomonodromic method. The
strategy consists of solving the Riemann-Hilbert map relating the accessory
parameters of the differential equations involved to monodromy properties of
the solutions, using the $\tau$-function for the Painlev\'e V transcendent. We
show good accordance of the method with the literature for generic rotation
parameter $a<M$. In the extremal limit, we determined the dependence of the
modes with the black hole temperature and establish that the extremal values of
the modes are obtainable from the Painlev\'e V and III transcendents. |
Scaling attractors in multi-field inflation: Multi-field inflation with a curved scalar geometry has been found to support
background trajectories that violate the slow-roll, slow-turn conditions and
thus have the potential to evade the swampland constraints. In order to
understand how generic this novel behaviour is and what conditions lead to it,
we perform a classification of dynamical attractors of two-field inflation that
are of the scaling type. Scaling solutions form a one-parameter generalization
of De Sitter solutions with a constant value of the first Hubble flow parameter
$\epsilon$ and, as we argue and demonstrate, form a natural starting point for
the study of non-slow-roll slow-turn behaviour.
All scaling solutions can be classified as critical points of a specific
dynamical system. We recover known multi-field inflationary attractors as
approximate scaling solutions and classify their stability using dynamical
system techniques. In particular, we discover that dynamical bifurcations play
an integral role in the transition between geodesic and non-geodesic motion and
discuss the ability of scaling solutions to describe realistic multi-field
models. We revisit the criteria for background stability and show cases where
the usual criteria found in the literature do not capture the background
evolution of the system. | Aether-scalar field compactification and Casimir effect: In this study, we explore the impact of an additional dimension, as proposed
in Kaluza-Klein's theory, on the Casimir effect within the context of Lorentz
invariance violation (LIV), which is represented by the aether field. We
demonstrate that the Casimir energy is directly influenced by the presence of
the fifth dimension, as well as by the aether parameter. Consequently, the
force between the plates is also subject to variations of these parameters.
Furthermore, we examine constraints on both the size of the extra dimension and
the aether field parameter based on experimental data. The LIV parameter can
provide insights into addressing the size-related challenges in Kaluza-Klein's
theory and offers a mean to establish an upper limit on the size of the extra
dimension. This helps to rationalize the difficulties associated with its
detection in current experiments. |
Line defects in the 3d Ising model: We investigate the properties of the twist line defect in the critical 3d
Ising model using Monte Carlo simulations. In this model the twist line defect
is the boundary of a surface of frustrated links or, in a dual description, the
Wilson line of the Z2 gauge theory. We test the hypothesis that the twist line
defect flows to a conformal line defect at criticality and evaluate numerically
the low-lying spectrum of anomalous dimensions of the local operators which
live on the defect as well as mixed correlation functions of local operators in
the bulk and on the defect. | Heterotic Line Bundle Models on Generalized Complete Intersection Calabi
Yau Manifolds: The systematic program of heterotic line bundle model building has resulted
in a wealth of standard-like models (SLM) for particle physics. In this paper,
we continue this work in the setting of generalised Complete Intersection
Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in Ref. [1], we
identify two geometries that, when combined with line bundle sums, are directly
suitable for heterotic GUT models. We then show that these gCICYs admit freely
acting $\mathbb{Z}_2$ symmetry groups, and are thus amenable to Wilson line
breaking of the GUT gauge group to that of the standard model. We proceed to a
systematic scan over line bundle sums over these geometries, that result in 99
and 33 SLMs, respectively. For the first class of models, our results may be
compared to line bundle models on homotopically equivalent Complete
Intersection Calabi Yau manifolds. This shows that the number of realistic
configurations is of the same order of magnitude. |
The modified Seiberg-Witten monopole equations and their exact solutions: The modified Seiberg-Witten monopole equations are presented in this letter.
These equations have analytic solutions in the whole 1+3 Minkowski space with
finite energy. The physical meaning of the equations and solutions are
discussed here. | Some classes of renormalizable tensor models: We identify new families of renormalizable of tensor models from anterior
renormalizable tensor models via a mapping capable of reducing or increasing
the rank of the theory without having an effect on the renormalizability
property. Mainly, a version of the rank 3 tensor model as defined in
[arXiv:1201.0176 [hep-th]], the Grosse-Wulkenhaar model in 4D and 2D generate
three different classes of renormalizable models. The proof of the
renormalizability is fully performed for the first reduced model. The same
procedure can be applied for the remaining cases. Interestingly, we find that,
due to the peculiar behavior of anisotropic wave function renormalizations, the
rank 3 tensor model reduced to a matrix model generates a simple
super-renormalizable vector model. |
Exact effective interactions and 1/4-BPS dyons in heterotic CHL
orbifolds: Motivated by precision counting of BPS black holes, we analyze six-derivative
couplings in the low energy effective action of three-dimensional string vacua
with 16 supercharges. Based on perturbative computations up to two-loop,
supersymmetry and duality arguments, we conjecture that the exact coefficient
of the $\nabla^2(\nabla\phi)^4$ effective interaction is given by a genus-two
modular integral of a Siegel theta series for the non-perturbative Narain
lattice times a specific meromorphic Siegel modular form. The latter is
familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact
degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known
perturbative corrections at weak heterotic coupling, including tree-level, one-
and two-loop corrections, plus non-perturbative effects of order
$e^{-1/g_3^2}$. We also examine the weak coupling expansions in type I and type
II string duals and find agreement with known perturbative results, as well as
new predictions for higher genus perturbative contributions. In the limit where
a circle in the internal torus decompactifies, our Ansatz predicts the exact
$\nabla^2 F^4$ effective interaction in four-dimensional CHL string vacua,
along with infinite series of exponentially suppressed corrections of order
$e^{-R}$ from Euclideanized BPS black holes winding around the circle, and
further suppressed corrections of order $e^{-R^2}$ from Taub-NUT instantons. We
show that instanton corrections from 1/4-BPS black holes are precisely weighted
by the BPS index predicted from the DVV formula, including the detailed moduli
dependence. We also extract two-instanton corrections from pairs of 1/2-BPS
black holes, demonstrating consistency with supersymmetry and wall-crossing,
and estimate the size of instanton-anti-instanton contributions. | Meta-Stable Brane Configurations with Multiple NS5-Branes: Starting from an N=1 supersymmetric electric gauge theory with the multiple
product gauge group and the bifundamentals, we apply Seiberg dual to each gauge
group, obtain the N=1 supersymmetric dual magnetic gauge theories with dual
matters including the gauge singlets. Then we describe the intersecting brane
configurations, where there are NS-branes and D4-branes(and anti D4-branes), of
type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua
of this gauge theory.
We also discuss the case where the orientifold 4-planes are added into the
above brane configuration. Next, by adding an orientifold 6-plane, we apply to
an N=1 supersymmetric electric gauge theory with the multiple product gauge
group(where a single symplectic or orthogonal gauge group is present) and the
bifundamentals. Finally, we describe the other cases where the orientifold
6-plane intersects with NS-brane. |
B-Model Approaches to Instanton Counting: This is the 13th article in the collection of reviews "Exact results in N=2
supersymmetric gauge theories", ed. J. Teschner. It discusses the relation
between the instanton partition functions and the partition function of the
topological string from the perspective of the B-model. The instanton partition
functions provide solutions to the holomorphic anomaly equations characterising
the partition functions of the topological string. | Odd entanglement entropy in Galilean conformal field theories and flat
holography: The odd entanglement entropy (OEE) for bipartite states in a class of
$(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) is
obtained through an appropriate replica technique. In this context our results
are compared with the entanglement wedge cross section (EWCS) for
$(2+1)$-dimensional asymptotically flat geometries dual to the $GCFT_{1+1}$ in
the framework of flat holography. We find that our results are consistent with
the duality of the difference between the odd entanglement entropy and the
entanglement entropy of bipartite states, with the bulk EWCS for flat
holographic scenarios. |
The quantum $p$-spin glass model: A user manual for holographers: We study a large-$N$ bosonic quantum mechanical sigma-model with a spherical
target space subject to disordered interactions, more colloquially known as the
$p$-spin spherical model. Replica symmetry is broken at low temperatures and
for sufficiently weak quantum fluctuations, which drives the system into a spin
glass phase. The first half of this paper is dedicated to a discussion of this
model's thermodynamics, with particular emphasis on the marginally stable spin
glass. This phase exhibits an emergent conformal symmetry in the strong
coupling regime, which dictates its thermodynamic properties. It is associated
with an extensive number of nearby states in the free energy landscape. We
discuss in detail an elegant approximate solution to the spin glass equations,
which interpolates between the conformal regime and an ultraviolet-complete
short distance solution. In the second half of this paper we explore the
real-time dynamics of the model and uncover quantum chaos as measured by
out-of-time-order four-point functions, both numerically and analytically. We
find exponential Lyapunov growth, which intricately depends on the model's
couplings and becomes strongest in the quantum critical regime. We emphasize
that the spin glass phase also exhibits quantum chaos, albeit with
parametrically smaller Lyapunov exponent than in the replica symmetric phase.
An analytical calculation in the marginal spin glass phase suggests that this
Lyapunov exponent vanishes in a particular infinite coupling limit. We comment
on the potential meaning of these observations from the perspective of
holography. | Gradient Properties of Perturbative Multiscalar RG Flows to Six Loops: The gradient property of the renormalisation group (RG) flow of multiscalar
theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions.
Such theories undergo RG flows in the space of quartic couplings $\lambda^I$.
Starting at five loops, the relevant vector field that determines the physical
RG flow is not the beta function traditionally computed in a minimal
subtraction scheme in dimensional regularisation, but a suitable modification
of it, the $B$ function. It is found that up to five loops the $B$ vector field
is gradient, i.e. $B^I=G^{IJ}\partial A / \partial\lambda^J$ with $A$ a scalar
and $G_{IJ}$ a rank-two symmetric tensor of the couplings. Up to five loops the
beta function is also gradient, but it fails to be so at six loops. The
conditions under which the $B$ function (and hence the RG flow) is gradient at
six loops are specified, but their verification rests on a separate six-loop
computation that remains to be performed. |
Implications of Lorentz symmetry violation on a 5D supersymmetric model: Field models with $n$ extra spatial dimensions have a larger $SO(1,3+n)$
Lorentz symmetry which is broken down to the standard $SO(1,3)$ four
dimensional one by the compactification process. By considering Lorentz
violating operators in a $5D$ supersymmetric Wess-Zumino mo\-del, which
otherwise conserve the standard four dimensional Poincare invariance, we show
that supersymmetry can be restored upon a simple deformation of the
supersymmetric transformations. However, supersymmetry is not preserved in the
effective $4D$ theory that arises after compactification when the $5D$ Lorentz
violating operators do not preserve $Z_2: y\rightarrow -y$ bulk parity. Our
mechanism unveils a possible connection among Lorentz violation and the
Scherk-Schwarz mechanism. We also show that parity preserving models, on the
other hand, do provide well defined supersymmetric KK models. | Triangle Anomalies, Thermodynamics, and Hydrodynamics: We consider 3+1-dimensional fluids with U(1)^3 anomalies. We use Ward
identities to constrain low-momentum Euclidean correlation functions and obtain
differential equations that relate two and three-point functions. The solution
to those equations yields, among other things, the chiral magnetic
conductivity. We then compute zero-frequency functions in hydrodynamics and
show that the consistency of the hydrodynamic theory also fixes the
anomaly-induced conductivities. |
Localised Anti-Branes in Flux Backgrounds: Solutions corresponding to finite temperature (anti)-D3 and M2 branes
localised in flux backgrounds are constructed in a linear approximation. The
flux backgrounds considered are toy models for the IR of the Klebanov-Strassler
solution and its M-theory analogue, the Cveti\v{c}-Gibbons-L\"{u}-Pope
solution. Smooth solutions exist for either sign charge, in stark contrast with
the previously considered case of smeared black branes. That the singularities
of the anti-branes in the zero temperature extremal limit can be shielded
behind a finite temperature horizon indicates that the singularities are
physical and resolvable by string theory. As the charge of the branes grows
large and negative, the flux at the horizon increases without bound and
diverges in the extremal limit, which suggests a resolution via brane
polarisation \`{a} la Polchinski-Strassler. It therefore appears that the
anti-brane singularities do not indicate a problem with the SUSY-breaking
metastable states corresponding to expanded anti-brane configurations in these
backgrounds, nor with the use of these states in constructing the de Sitter
landscape. | New Double Soft Emission Theorems: We study the behavior of the tree-level S-matrix of a variety of theories as
two particles become soft. By analogy with the recently found subleading soft
theorems for gravitons and gluons, we explore subleading terms in double soft
emissions. We first consider double soft scalar emissions and find subleading
terms that are controlled by the angular momentum operator acting on hard
particles. The order of the subleading theorems depends on the presence or not
of color structures. Next we obtain a compact formula for the leading term in a
double soft photon emission. The theories studied are a special Galileon, DBI,
Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found
CHY representation of these theories in order to give a simple proof of the
leading order part of all these theorems |
Quantum and Braided Linear Algebra: Quantum matrices $A(R)$ are known for every $R$ matrix obeying the Quantum
Yang-Baxter Equations. It is also known that these act on `vectors' given by
the corresponding Zamalodchikov algebra. We develop this interpretation in
detail, distinguishing between two forms of this algebra, $V(R)$ (vectors) and
$V^*(R)$ (covectors). $A(R)\to V(R_{21})\tens V^*(R)$ is an algebra
homomorphism (i.e. quantum matrices are realized by the tensor product of a
quantum vector with a quantum covector), while the inner product of a quantum
covector with a quantum vector transforms as a scaler. We show that if $V(R)$
and $V^*(R)$ are endowed with the necessary braid statistics $\Psi$ then their
braided tensor-product $V(R)\und\tens V^*(R)$ is a realization of the braided
matrices $B(R)$ introduced previously, while their inner product leads to an
invariant quantum trace. Introducing braid statistics in this way leads to a
fully covariant quantum (braided) linear algebra. The braided groups obtained
from $B(R)$ act on themselves by conjugation in a way impossible for the
quantum groups obtained from $A(R)$. | Energy-energy correlations at next-to-next-to-leading order: We develop further an approach to computing energy-energy correlations (EEC)
directly from finite correlation functions. In this way, one completely avoids
infrared divergences. In maximally supersymmetric Yang-Mills theory
($\mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the
EEC to a triple discontinuity of a four-point correlation function. We use this
formula to compute the EEC in $\mathcal{N}=4$ sYM at next-to-next-to-leading
order in perturbation theory. Our result is given by a two-fold integral
representation that is straightforwardly evaluated numerically. We find that
some of the integration kernels are equivalent to those appearing in sunrise
Feynman integrals, which evaluate to elliptic functions. Finally, we use the
new formula to provide the expansion of the EEC in the back-to-back and
collinear limits. |
Superstring in doubled superspace: The covariant and kappa-symmetric action for superstring in direct product of
two flat D=10 N=1 superspaces is presented. It is given by the sum of
supersymmetric generalization of two copies of chiral boson actions constructed
with the use of the Pasti-Sorokin-Tonin (PST) technique. The chirality of 8
`left' bosons and 8 `left' fermions and the anti-chirality of their `right'
counterparts are obtained as gauge fixed version of the equations of motion, so
that the physical degrees of freedom are essentially those of the II
Green-Schwarz superstring. Our action is manifestly T-duality invariant as the
fields describing oscillating and winding modes enter it on equal footing. | Consistent SO(6) Reduction Of Type IIB Supergravity on S^5: Type IIB supergravity can be consistently truncated to the metric and the
self-dual 5-form. We obtain the complete non-linear Kaluza-Klein S^5 reduction
Ansatz for this theory, giving rise to gravity coupled to the fifteen
Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset
SL(6,R)/SO(6). This provides a consistent embedding of this subsector of N=8,
D=5 gauged supergravity in type IIB in D=10. We demonstrate that the
self-duality of the 5-form plays a crucial role in the consistency of the
reduction. We also discuss certain necessary conditions for a theory of gravity
and an antisymmetric tensor in an arbitrary dimension D to admit a consistent
sphere reduction, keeping all the massless fields. We find that it is only
possible for D=11, with a 4-form field, and D=10, with a 5-form. Furthermore,
in D=11 the full bosonic structure of eleven-dimensional supergravity is
required, while in D=10 the 5-form must be self-dual. It is remarkable that
just from the consistency requirement alone one would discover D=11 and type
IIB supergravities, and that D=11 is an upper bound on the dimension. |
New Consistent Limits to M-theory: The construction of effective field theories describing M-theory compactified
on $S^1/{\bf Z}_2$ is revisited, and new insights into the parameters of the
theory are explained. Particularly, the web of constraints which follow from
supersymmetry and anomaly cancelation is argued to be more rich than previously
understood. In contradistinction to the lore on the subject, a consistent
classical theory describing the coupling of eleven dimensional supergravity to
super Yang-Mills theory constrained to the orbifold fixed points is suggested
to exist. | Exact Three Dimensional Black Holes in String Theory: A black hole solution to three dimensional general relativity with a negative
cosmological constant has recently been found. We show that a slight
modification of this solution yields an exact solution to string theory. This
black hole is equivalent (under duality) to the previously discussed three
dimensional black string solution. Since the black string is asymptotically
flat and the black hole is asymptotically anti-de Sitter, this suggests that
strings are not affected by a negative cosmological constant in three
dimensions. |
Anomalies of Generalized Symmetries from Solitonic Defects: We propose the general idea that 't Hooft anomalies of generalized global
symmetries can be understood in terms of the properties of solitonic defects,
which generically are non-topological defects. The defining property of such
defects is that they act as sources for background fields of generalized
symmetries. 't Hooft anomalies arise when solitonic defects are charged under
these generalized symmetries. We illustrate this idea for several kinds of
anomalies in various spacetime dimensions. A systematic exploration is
performed in 3d for 0-form, 1-form, and 2-group symmetries, whose 't Hooft
anomalies are related to two special types of solitonic defects, namely vortex
line defects and monopole operators. This analysis is supplemented with
detailed computations of such anomalies in a large class of 3d gauge theories.
Central to this computation is the determination of the gauge and 0-form
charges of a variety of monopole operators: these involve standard gauge
monopole operators, but also fractional gauge monopole operators, as well as
monopole operators for 0-form symmetries. The charges of these monopole
operators mainly receive contributions from Chern-Simons terms and fermions in
the matter content. Along the way, we interpret the vanishing of the global
gauge and ABJ anomalies, which are anomalies not captured by local anomaly
polynomials, as the requirement that gauge monopole operators and mixed
monopole operators for 0-form and gauge symmetries have non-fractional integer
charges. | Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory: We study the U(N) non-commutative Yang-Mills theory at the one-loop
approximation. We check renormalizability and gauge invariance of the model and
calculate the one-loop beta function. The interaction of the SU(N) gauge bosons
with the U(1) gauge boson plays an important role in the consistency check. In
particular, the SU(N) theory by itself is not consistent. We also find that the
theta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x
U(1) commutative theory, even at the planar limit. Finally, we comment on the
UV/IR mixing. |
Vacuum Polarization of STU Black Holes and their Subtracted Geometry
Limit: We study the vacuum polarization of a massless minimally coupled scalar field
at the horizon of four-charge STU black holes. We compare the results for the
standard asymptotically flat black holes and for the black holes obtained in
the "subtracted limit", both in the general static case and at the horizon pole
for the general rotating case. The original and the subtracted results are
identical only in the BPS limit, and have opposite sign in the extremal Kerr
limit. We also compute the vacuum polarization on the static solutions that
interpolate between both the original and the subtracted case through a
solution-generating transformation and show that the vacuum polarization stays
positive throughout the interpolating solution. In the Appendix we provide a
closed-form solution for the Green's function on general (static or rotating)
subtracted black hole geometries. | Liquid crystal defects and confinement in Yang-Mills theory: We show that in the Landau gauge of the SU(2) Yang-Mills theory the residual
global symmetry supports existence of the topological vortices which resemble
disclination defects in the nematic liquid crystals and the Alice
(half-quantum) vortices in the superfluid heluim 3 in the A-phase. The theory
also possesses half-integer and integer charged monopoles which are analogous
to the point-like defects in the nematic crystal and in the liquid helium. We
argue that the deconfinement phase transition in the Yang-Mills theory in the
Landau gauge is associated with the proliferation of these vortices and/or
monopoles. The disorder caused by these defects is suggested to be responsible
for the confinement of quarks in the low-temperature phase. |
Anomaly breaking of de Sitter symmetry: To one loop order, interacting boson fields on de Sitter space have an
"infrared" anomaly that breaks the de Sitter symmetry for all vacua save the
Euclidian one. The divergence of a symmetry current at point $x$ has a non-zero
contribution at the antipodal point ${\bar x}$. | Flux-branes and the Dielectric Effect in String Theory: We consider the generalization to String and M-theory of the Melvin solution.
These are flux p-branes which have (p+1)-dimensional Poincare invariance and
are associated to an electric (p+1)-form field strength along their
worldvolume. When a stack of Dp-branes is placed along the worldvolume of a
flux (p+3)-brane it will expand to a spherical D(p+2)-brane due to the
dielectric effect. This provides a new setup to consider the gauge
theory/gravity duality. Compactifying M-theory on a circle we find the exact
gravity solution of the type IIA theory describing the dielectric expansion of
N D4-branes into a spherical bound state of D4-D6-branes, due to the presence
of a flux 7-brane. In the decoupling limit, the deformation of the dual field
theory associated with the presence of the flux brane is irrelevant in the UV.
We calculate the gravitational radius and energy of the dielectric brane which
give, respectively, a prediction for the VEV of scalars and vacuum energy of
the dual field theory. Consideration of a spherical D6-brane probe with n units
of D4-brane charge in the dielectric brane geometry suggests that the dual
theory arises as the Scherk-Schwarz reduction of the M5-branes (2,0) conformal
field theory. The probe potential has one minimum placed at the locus of the
bulk dielectric brane and another associated to an inner dielectric brane
shell. |
Correlation Functions of Complex Matrix Models: For a restricted class of potentials (harmonic+Gaussian potentials), we
express the resolvent integral for the correlation functions of simple traces
of powers of complex matrices of size $N$, in term of a determinant; this
determinant is function of four kernels constructed from the orthogonal
polynomials corresponding to the potential and from their Cauchy transform. The
correlation functions are a sum of expressions attached to a set of fully
packed oriented loops configurations; for rotational invariant systems,
explicit expressions can be written for each configuration and more
specifically for the Gaussian potential, we obtain the large $N$ expansion ('t
Hooft expansion) and the so-called BMN limit. | Comments on Higher Derivative Operators in Some SUSY Field Theories: We study the leading irrelevant operators along the flat directions of
certain supersymmetric theories. In particular, we focus on finite N=2
(including N=4) supersymmetric field theories in four dimensions and show that
these operators are completely determined by the symmetries of the problem.
This shows that they are generated only at one loop and are not renormalized
beyond this order. An instanton computation in similar three dimensional
theories shows that these terms are renormalized. Hence, the four dimensional
non-renormalization theorem of these terms is not valid in three dimensions. |
A Consistency Relation for Single-Field Inflation with Power Spectrum
Oscillations: We derive a theoretical upper bound on the oscillation frequency in the
scalar perturbation power spectrum of single-field inflation. Oscillations are
most naturally produced by modified vacua with varying phase. When this phase
changes rapidly, it induces strong interactions between the scalar
fluctuations. If the interactions are sufficiently strong the theory cannot be
evaluated using perturbation theory, hence imposing a limit on the oscillation
frequency. This complements the bound found by Weinberg governing the validity
of effective field theory. The generalized consistency relation also allows one
to use squeezed configurations of higher-point correlations to place
constraints on the power spectrum oscillations. | Missing Mirrors: Type IIA Supergravity on the Resolved Conifold: We consider massive IIA supergravity on the resolved conifold with
$SU(2)_L^2\times U(1)_R$ symmetry and $\N=1$ supersymmetry. A one dimensional
family of such regular solutions was found by Brandhuber and we propose this to
be the mirror to one dimension of the moduli space of IIB solutions on the
deformed conifold found by Butti et al. This family provides a description of
the geometric transition in terms of a smooth family of flux backgrounds. The
remaining dimension of the moduli space of Butti et al contains the baryonic
branch of Klebanov-Strassler and we propose that the mirror of this is either
some stringy resolution of a family of singular solutions found here or must be
entirely non-geometric. |
Gauged compact Q-balls and Q-shells in a multi-component $CP^N$ model: We study a multicomponent $CP^N$ model's scalar electrodynamics. The model
contains Q-balls/shells, which are non-topological compact solitons with time
dependency $e^{i\omega t}$. Two coupled $CP^N$ models can decouple locally if
one of their $CP^N$ fields takes the vacuum value. Because of the compacton
nature of solutions, Q-shells can shelter another compact Q-ball or Q-shell
within their hollow region. Even if compactons do not overlap, they can
interact through the electromagnetic field. We investigate how the size of
multi-compacton formations is affected by electric charge. We are interested in
structures with non-zero or zero total net charge. | Minimal Simple de Sitter Solutions: We show that the minimal set of necessary ingredients to construct explicit,
four-dimensional de Sitter solutions from IIA string theory at tree-level are
O6-planes, non-zero Romans mass parameter, form fluxes, and negative internal
curvature. To illustrate our general results, we construct such minimal simple
de Sitter solutions from an orientifold compactification of compact hyperbolic
spaces. In this case there are only two moduli and we demonstrate that they are
stabilized to a sufficiently weakly coupled and large volume regime. We also
discuss generalizations of the scenario to more general metric flux
constructions. |
Quantum chains with a Catalan tree pattern of conserved charges: the
$Δ= -1$ XXZ model and the isotropic octonionic chain: A class of quantum chains possessing a family of local conserved charges with
a Catalan tree pattern is studied. Recently, we have identified such a
structure in the integrable $SU(N)$-invariant chains. In the present work we
find sufficient conditions for the existence of a family of charges with this
structure in terms of the underlying algebra. Two additional systems with a
Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ
model with $\Delta=-1$. The other is a new octonionic isotropic chain,
generalizing the Heisenberg model. This system provides an interesting example
of an infinite family of noncommuting local conserved quantities. | Formation of Chiral Soliton Lattice: The Chiral Soliton Lattice (CSL) is a lattice structure composed of domain
walls aligned in parallel at equal intervals, which is energetically stable in
the presence of a background magnetic field and a finite (baryon) chemical
potential due to the topological term originated from the chiral anomaly. We
study its formation from the vacuum state, with describing the CSL as a layer
of domain-wall disks surrounded by the vortex or string loop, based on the
Nambu-Goto-type effective theory. We show that the domain wall nucleates via
quantum tunneling when the magnetic field is strong enough. We evaluate its
nucleation rate and determine the critical magnetic field strength with which
the nucleation rate is no longer exponentially suppressed. We apply this
analysis to the neutral pion in the two-flavor QCD as well as the axion-like
particles (ALPs) with a finite (baryon) chemical potential under an external
magnetic field. In the former case, even though the CSL state is more
energetically stable than the vacuum state and the nucleation rate becomes
larger for sufficiently strong magnetic field, it cannot be large enough so
that the nucleation of the domain walls is not exponentially suppressed and
promoted, without suffering from the tachyonic instability of the charged pion
fluctuations. In the latter case, we confirm that the effective interaction of
the ALPs generically includes the topological term required for the CSL state
to be energetically favored. We show that the ALP CSL formation is promoted if
the magnetic field strength and the chemical potential of the system is
slightly larger than the scale of the axion decay constant. |
Non-canonical quantization of electromagnetic fields and the meaning of
$Z_3$: Non-canonical quantization is based on certain reducible representations of
canonical commutation relations. Relativistic formalism for electromagnetic
non-canonical quantum fields is introduced. Unitary representations of the
Poincar\'e group at the level of fields and states are explicitly given.
Multi-photon and coherent states are introduced. Statistics of photons in a
coherent state is Poissonian if an appropriately defined thermodynamic limit is
performed. Radiation fields having a correct $S$ matrix are constructed. The
$S$ matrix is given by a non-canonical coherent-state displacement operator, a
fact automatically eliminating the infrared catastrophe. This, together with
earlier results on elimination of vacuum and ultraviolet infinities, suggests
that non-canonical quantization leads to finite field theories. Renormalization
constant $Z_3$ is found as a parameter related to wave functions of
non-canonical vacua. | Quartic Horndeski, planar black holes, holographic aspects and universal
bounds: In this work, we consider a specific shift-invariant quartic Horndeski model,
deriving new planar black hole solutions with axionic hair. We explore these
solutions in terms of their horizon structure and their thermodynamic
properties. We use the gauge/gravity dictionary to derive the DC transport
coefficients of the holographic dual with the aim of investigating how the new
deformation affects the universality of some renown bound proposals. Although
most of them are found to hold true, we nevertheless find a highly interesting
parametric violation of the heat conductivity-to-temperature lower bound which
acquires a dependence on both the scale and the coupling. Finally, using a
perturbative approach, a more brutal violation of the viscocity-to-entropy
ratio is demonstrated. |
Celestial Operator Products of Gluons and Gravitons: The operator product expansion (OPE) on the celestial sphere of conformal
primary gluons and gravitons is studied. Asymptotic symmetries imply recursion
relations between products of operators whose conformal weights differ by
half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that
these recursion relations are so constraining that they completely fix the
leading celestial OPE coefficients in terms of the Euler beta function. The
poles in the beta functions are associated with conformally soft currents. | Q-holes: We consider localized soliton-like solutions in the presence of a stable
scalar condensate background. By the analogy with classical mechanics, it can
be shown that there may exist solutions of the nonlinear equations of motion
that describe dips or rises in the spatially-uniform charge distribution. We
also present explicit analytical solutions for some of such objects and examine
their properties. |
Classical and Quantum Integrable Systems in $\wt{\gr{gl}}(2)^{+*}$ and
Separation of Variables: Classical integrable Hamiltonian systems generated by elements of the Poisson
commuting ring of spectral invariants on rational coadjoint orbits of the loop
algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of
variables in the Hamilton-Jacobi equation in hyperellipsoidal coordinates. The
canonically quantized systems are then shown to also be completely integrable
and separable within the same coordinates. Pairs of second class constraints
defining reduced phase spaces are implemented in the quantized systems by
choosing one constraint as an invariant, and interpreting the other as
determining a quotient (i.e., by treating one as a first class constraint and
the other as a gauge condition). Completely integrable, separable systems on
spheres and ellipsoids result, but those on ellipsoids require a further
modification of order $\OO(\hbar^2)$ in the commuting invariants in order to
assure self-adjointness and to recover the Laplacian for the case of free
motion. For each case - in the ambient space ${\bf R}^{n}$, the sphere and the
ellipsoid - the Schr\"odinger equations are completely separated in
hyperellipsoidal coordinates, giving equations of generalized Lam\'e type. | Matching the observational value of the cosmological constant: A simple model is introduced in which the cosmological constant is
interpreted as a true Casimir effect on a scalar field filling the universe
(e.g. $\mathbf{R} \times \mathbf{T}^p\times \mathbf{T}^q$, $\mathbf{R} \times
\mathbf{T}^p\times \mathbf{S}^q, ...$). The effect is driven by compactifying
boundary conditions imposed on some of the coordinates, associated both with
large and small scales. The very small -but non zero- value of the cosmological
constant obtained from recent astrophysical observations can be perfectly
matched with the results coming from the model, by playing just with the
numbers of -actually compactified- ordinary and tiny dimensions, and being the
compactification radius (for the last) in the range $(1-10^3) l_{Pl}$, where
$l_{Pl}$ is the Planck length. This corresponds to solving, in a way, what has
been termed by Weinberg the {\it new} cosmological constant problem. Moreover,
a marginally closed universe is favored by the model, again in coincidence with
independent analysis of the observational results. |
Hopf Solitons on the Lattice: Hopf solitons in the Skyrme-Faddeev model -- S^2-valued fields on R^3 with
Skyrme dynamics -- are string-like topological solitons. In this Letter, we
investigate the analogous lattice objects, for S^2-valued fields on the cubic
lattice Z^3 with a nearest-neighbour interaction. For suitable choices of the
interaction, topological solitons exist on the lattice. Their appearance is
remarkably similar to that of their continuum counterparts, and they exhibit
the same power-law relation E \approx c H^{3/4} between the energy E and the
Hopf number H. | Tachyon-free Orientifolds of Type 0B Strings in Various Dimensions: We construct non-tachyonic, non-supersymmetric orientifolds of Type 0B
strings in ten, six and four space-time dimensions. Typically, these models
have unitary gauge groups with charged massless fermionic and bosonic matter
fields. However, generically there remains an uncancelled dilaton tadpole. |
Quantum anomalies and some recent developments: Some of the developments related to quantum anomalies and path integrals
during the past 10 years are briefly discussed. The covered subjects include
the issues related to the local counter term in the context of 2-dimensional
path integral bosonization and the treatment of chiral anomaly and index
theorem on the lattice. We also briefly comment on a recent analysis of the
connection between the two-dimensional chiral anomalies and the
four-dimensional black hole radiation. | Touching Random Surfaces and Liouville Gravity: Large $N$ matrix models modified by terms of the form $ g(\Tr\Phi^n)^2$
generate random surfaces which touch at isolated points. Matrix model results
indicate that, as $g$ is increased to a special value $g_t$, the string
susceptibility exponent suddenly jumps from its conventional value $\gamma$ to
${\gamma\over\gamma-1}$. We study this effect in \L\ gravity and attribute it
to a change of the interaction term from $O e^{\alpha_+ \phi}$ for $g<g_t$ to
$O e^{\alpha_- \phi}$ for $g=g_t$ ($\alpha_+$ and $\alpha_-$ are the two roots
of the conformal invariance condition for the \L\ dressing of a matter operator
$O$). Thus, the new critical behavior is explained by the unconventional branch
of \L\ dressing in the action. |
Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at
Weak Coupling: In this paper we consider a special kind of three-point functions of HHL type
at weak coupling in N=4 SYM theory and analyze its volume dependence. At strong
coupling this kind of three-point functions were studied recently by Bajnok,
Janik and Wereszczynski [1]. The authors considered some cases of HHL
correlator in the su(2) sector and, relying on their explicit results,
formulated a conjecture about the form of the volume dependence of the
symmetric HHL structure constant to be valid at any coupling up to wrapping
corrections. In order to test this hypothesis we considered the HHL correlator
in su(2) sector at weak coupling and directly showed that, up to one loop, the
finite volume dependence has exactly the form proposed in [1]. Another side of
the conjecture suggests that computation of the symmetric structure constant is
equivalent to computing the corresponding set of infinite volume form factors,
which can be extracted as the coefficients of finite volume expansion. In this
sense, extracting appropriate coefficients from our result gives a prediction
for the corresponding infinite volume form factors. | Supersymmetric Toda Field Theories: We present new supersymmetric extensions of Conformal Toda and $A^{(1)}_N$
Affine Toda field theories. These new theories are constructed using methods
similar to those that have been developed to find supersymmetric extensions of
two-dimensional bosonic sigma models with a scalar potential. In particular, we
show that the Conformal Toda field theory admits a (1,1)-supersymmetric
extension, and the $A^{(1)}_N$ Affine Toda field admits a (1,0)-supersymmetric
extension. |
Brane-anti-brane Democracy: We suggest a duality invariant formula for the entropy and temperature of
non-extreme black holes in supersymmetric string theory. The entropy is given
in terms of the duality invariant parameter of the deviation from extremality
and 56 SU(8) covariant central charges. It interpolates between the entropies
of Schwarzschild solution and extremal solutions with various amount of
unbroken supersymmetries and therefore serves for classification of black holes
in supersymmetric string theories. We introduce the second auxiliary 56 via
E(7) symmetric constraint. The symmetric and antisymmetric combinations of
these two multiplets are related via moduli to the corresponding two
fundamental representations of E(7): brane and anti-brane "numbers." Using the
CPT as well as C symmetry of the entropy formula and duality one can explain
the mysterious simplicity of the non-extreme black hole area formula in terms
of branes and anti-branes. | A quasi-particle description of the M(3,p) models: The M(3,p) minimal models are reconsidered from the point of view of the
extended algebra whose generators are the energy-momentum tensor and the
primary field \phi_{2,1} of dimension $(p-2)/4$. Within this framework, we
provide a quasi-particle description of these models, in which all states are
expressed solely in terms of the \phi_{2,1}-modes. More precisely, we show that
all the states can be written in terms of \phi_{2,1}-type highest-weight states
and their phi_{2,1}-descendants. We further demonstrate that the conformal
dimension of these highest-weight states can be calculated from the \phi_{2,1}
commutation relations, the highest-weight conditions and associativity. For the
simplest models (p=5,7), the full spectrum is explicitly reconstructed along
these lines. For $p$ odd, the commutation relations between the \phi_{2,1}
modes take the form of infinite sums, i.e., of generalized commutation
relations akin to parafermionic models. In that case, an unexpected operator,
generalizing the Witten index, is unravelled in the OPE of \phi_{2,1} with
itself. A quasi-particle basis formulated in terms of the sole \phi_{1,2} modes
is studied for all allowed values of p. We argue that it is governed by
jagged-type partitions further subject a difference 2 condition at distance 2.
We demonstrate the correctness of this basis by constructing its generating
function, from which the proper fermionic expression of the combination of the
Virasoro irreducible characters \chi_{1,s} and \chi_{1,p-s} (for 1\leq s\leq
[p/3]+1) are recovered. As an aside, a practical technique for implementing
associativity at the level of mode computations is presented, together with a
general discussion of the relation between associativity and the Jacobi
identities. |
Brane-worlds and their Deformations: A geometric theory of brane-worlds with large or non-compact extra dimensions
is presented. It is shown that coordinate gauge independent perturbations of
the brane-world correspond to the Einstein-Hilbert dynamics derived from the
embeddings of the brane-world. The quantum states of a perturbation are
described by Schr\"odinger's equation with respect to the extra dimensions and
the deformation Hamiltonian. A gauge potential with confined components is
derived from the differentiable structure of the brane-world | Faster than Hermitian Time Evolution: For any pair of quantum states, an initial state |I> and a final quantum
state |F>, in a Hilbert space, there are many Hamiltonians H under which |I>
evolves into |F>. Let us impose the constraint that the difference between the
largest and smallest eigenvalues of H, E_max and E_min, is held fixed. We can
then determine the Hamiltonian H that satisfies this constraint and achieves
the transformation from the initial state to the final state in the least
possible time \tau. For Hermitian Hamiltonians, \tau has a nonzero lower bound.
However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same
energy constraint, \tau can be made arbitrarily small without violating the
time-energy uncertainty principle. The minimum value of \tau can be made
arbitrarily small because for PT-symmetric Hamiltonians the path from the
vector |I> to the vector |F>, as measured using the Hilbert-space metric
appropriate for this theory, can be made arbitrarily short. The mechanism
described here is similar to that in general relativity in which the distance
between two space-time points can be made small if they are connected by a
wormhole. This result may have applications in quantum computing. |
Induced modules for vertex operator algebras: For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which
is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a
$g$-twisted induction functor from the category of $g$-twisted $V'$-modules to
the category of $g$-twisted $V$-modules. This functor satisfies the Frobenius
reciprocity and transitivity. The results are illustrated with $V$ being simple
or with $V'$ being $g$-rational. | Supergravity Instantons and the Universal Hypermultiplet: The effective action of N=2 supersymmetric 5-dimensional supergravity arising
from compactifications of M-theory on Calabi-Yau threefolds receives
non-perturbative corrections from wrapped Euclidean membranes and fivebranes.
These contributions can be interpreted as instanton corrections in the 5
dimensional field theory. Focusing on the universal hypermultiplet, a solution
of this type is presented and the instanton action is calculated, generalizing
previous results involving membrane instantons. The instanton action is not a
sum of membrane and fivebrane contributions: it has the form reminiscent of
non-threshold bound states. |
I-Brane Inflow and Anomalous Couplings on D-Branes: We show that the anomalous couplings of $D$-brane gauge and gravitational
fields to Ramond-Ramond tensor potentials can be deduced by a simple anomaly
inflow argument applied to intersecting $D$-branes and use this to determine
the eight-form gravitational coupling. | Exact S-Matrices for Nonsimply-Laced Affine Toda Theories: We derive exact, factorized, purely elastic scattering matrices for affine
Toda theories based on the nonsimply-laced Lie algebras and superalgebras. |
Yang-Mills Instanton Sheaves with Higher Topological Charges: We explicitly construct SL(2,C) Yang-Mills (weakly) three and four instanton
sheaves on CP^3. These results extend the previous construction of Yang-Mills
(weakly) instanton sheaves with topological charge two [18]. | Aspects of the ODE/IM correspondence: We review a surprising correspondence between certain two-dimensional
integrable models and the spectral theory of ordinary differential equations.
Particular emphasis is given to the relevance of this correspondence to certain
problems in PT-symmetric quantum mechanics. |
The noncommutative sine-Gordon breather: As shown in [hep-th/0406065], there exists a noncommutative deformation of
the sine-Gordon model which remains (classically) integrable but features a
second scalar field. We employ the dressing method (adapted to the
Moyal-deformed situation) for constructing the deformed kink-antikink and
breather configurations. Explicit results and plots are presented for the
leading noncommutativity correction to the breather. Its temporal periodicity
is unchanged. | Cosmic string interactions induced by gauge and scalar fields: We study the interaction between two parallel cosmic strings induced by gauge
fields and by scalar fields with non-minimal couplings to curvature. For small
deficit angles the gauge field behaves like a collection of non-minimal scalars
with a specific value for the non-minimal coupling. We check this equivalence
by computing the interaction energy between strings at first order in the
deficit angles. This result provides another physical context for the "contact
terms" which play an important role in the renormalization of black hole
entropy due to a spin-1 field. |
Equation of State for a van der Waals Universe during Reissner-Nordstrom
Expansion: In a previous work [E.M. Prodanov, R.I. Ivanov, and V.G. Gueorguiev,
Reissner-Nordstrom Expansion, Astroparticle Physics 27 (150-154) 2007], we
proposed a classical model for the expansion of the Universe during the
radiation-dominated epoch based on the gravitational repulsion of the
Reissner-Nordstrom geometry - naked singularity description of particles that
"grow" with the drop of the temperature. In this work we model the Universe
during the Reissner-Nordstrom expansion as a van der Waals gas and determine
the equation of state. | Soliton Gauge States and T-duality of Closed Bosonic String Compatified
on Torus: We study soliton gauge states in the spectrum of bosonic string compatified
on torus. The enhenced Kac-Moody gauge symmetry, and thus T-duality, is shown
to be related to the existence of these soliton gauge states in some moduli
points. |
Ferromagnetic instability in PAAI in the sky: We study an idealised plasma of fermions, coupled through an abelian gauge
force $U(1)_X$, and which is asymmetric in that the masses of the oppositely
charged species are greatly unequal. The system is dubbed PAAI, plasma
asym\'etrique, ab\'elien et id\'ealis\'e. It is argued that due to the
ferromagnetic instability that arises, the ground state gives rise to a complex
of domain walls. This complex being held together by stresses much stronger
than cosmic gravity, does not evolve with the scale factor and along with the
heavier oppositely charged partners simulates the required features of Dark
Energy with mass scale for the lighter fermions in the micro-eV to nano-eV
range. Further, residual $X$-magnetic fields through mixture with standard
magnetic fields, can provide the seed for cosmic-scale magnetic fields. Thus
the scenario can explain several cosmological puzzles including Dark Energy. | Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with
Adjoint Fermions: A study of two-dimensional QCD on a spatial circle with Majorana fermions in
the adjoint representation of the gauge groups SU(2) and SU(3) has been
performed. The main emphasis is put on the symmetry properties related to the
homotopically non-trivial gauge transformations and the discrete axial symmetry
of this model. Within a gauge fixed canonical framework, the delicate interplay
of topology on the one hand and Jacobians and boundary conditions arising in
the course of resolving Gauss's law on the other hand is exhibited. As a
result, a consistent description of the residual $Z_N$ gauge symmetry (for
SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum
of the model is determined analytically in the limit of a small circle. There,
the Born-Oppenheimer approximation is justified and reduces the vacuum problem
to simple quantum mechanics. The issue of fermion condensates is addressed and
residual discrepancies with other approaches are pointed out. |
Pauli Oscillator In Noncommutative Space: In this study, we investigate the Pauli oscillator in a noncommutative space.
In other words, we derive wave function and energy spectrum of a spin half
non-relativistic charged particle that is moving under a constant magnetic
field with an oscillator potential in noncommutative space. We obtain critical
values of the deformation parameter and the magnetic field, which counteract
the normal and anomalous Zeeman effects. Moreover, we find that the deformation
parameter has to be smaller than $2.57\times 10^{-26}m^2$. Then, we derive the
Helmholtz free energy, internal energy, specific heat, and entropy functions of
the Pauli oscillator in the noncommutative space. With graphical methods, at
first, we compare these functions with the ordinary ones, and then, we
demonstrate the effects of magnetic field on these thermodynamic functions in
the commutative and noncommutative space, respectively | Universal Kounterterms in Lovelock AdS gravity: We show the universal form of the boundary term (Kounterterm series) which
regularizes the Euclidean action and background-independent definition of
conserved quantities for any Lovelock gravity theory with AdS asymptotics
(including Einstein-Hilbert and Einstein-Gauss-Bonnet). We discuss on the
connection of this procedure to the existence of topological invariants and
Chern-Simons forms in the corresponding dimensions. |
Deformations of calibrated D-branes in flux generalized complex
manifolds: We study massless deformations of generalized calibrated cycles, which
describe, in the language of generalized complex geometry, supersymmetric
D-branes in N=1 supersymmetric compactifications with fluxes. We find that the
deformations are classified by the first cohomology group of a Lie algebroid
canonically associated to the generalized calibrated cycle, seen as a
generalized complex submanifold with respect to the integrable generalized
complex structure of the bulk. We provide examples in the SU(3) structure case
and in a `genuine' generalized complex structure case. We discuss cases of
lifting of massless modes due to world-volume fluxes, background fluxes and a
generalized complex structure that changes type. | BCJ relations in ${AdS}_5 \times S^3$ and the double-trace spectrum of
super gluons: We revisit the four-point function of super gluons in $AdS_5 \times S^3$ in
the spirit of the large $p$ formalism and show how the integrand of a
generalised Mellin transform satisfies various non-trivial properties such as
$U(1)$ decoupling identity, BCJ relations and colour-kinematic duality, in a
way that directly mirrors the analogous relations in flat space. We unmix the
spectrum of double-trace operators at large $N$ and find all anomalous
dimensions at leading order. The anomalous dimensions follow a very simple
pattern, resembling those of other theories with hidden conformal symmetries. |
Universality of critical magnetic field in holographic superconductor: In this letter we study aspects of the holographic superconductors
analytically in the presence of a constant external magnetic field. We show
that the critical temperature and critical magnetic field can be calculated at
nonzero temperature. We detect the Meissner effect in such superconductors. A
universal relation between black hole mass $ M$ and critical magnetic field
$H_c$ is proposed as $\frac{H_c}{M^{2/3}}\leq 0.687365$. We discuss some
aspects of phase transition in terms of black hole entropy and the Bekenstein's
entropy to energy upper bound. | Heterotic Moduli Stabilisation: We perform a systematic analysis of moduli stabilisation for weakly coupled
heterotic string theory compactified on manifolds which are Calabi-Yau up to
alpha' effects. We review how to fix all geometric and bundle moduli in a
supersymmetric way by fractional fluxes, the requirement of a holomorphic gauge
bundle, D-terms, higher order perturbative contributions to W, non-perturbative
and threshold effects. We then show that alpha' corrections to K lead to new
stable Minkowski (or dS) vacua where the complex structure moduli Z and the
dilaton are fixed supersymmetrically, while the fixing of the Kahler moduli at
a lower scale leads to spontaneous SUSY breaking. The minimum lies at
moderately large volumes of all geometric moduli, at a perturbative string
coupling and at the right value of the GUT coupling. We also give a dynamical
derivation of anisotropic compactifications which allow for gauge coupling
unification around 10^16 GeV. The gravitino mass can be anywhere between the
GUT and TeV scale depending on the fixing of the Z-moduli. In general, these
are fixed by turning on background fluxes, leading to a gravitino mass around
the GUT scale since the heterotic 3-form flux does not contain enough freedom
to tune W to small values. Moreover accommodating the observed value of the
cosmological constant (CC) is a challenge. Low-energy SUSY could instead be
obtained in particular situations where the gauge bundle is holomorphic only at
a point-like sub-locus of Z-moduli space, or where the number of Z-moduli is
small (like orbifold models), since in these cases one may fix all moduli
without turning on any quantised flux. However tuning the CC is even more of a
challenge in these cases. Another option is to focus on non-complex manifolds
since these allow for new geometric fluxes which can be used to tune W and the
CC, even if their moduli space is presently only poorly understood. |
Vacuum fluctuation effects due to an Abelian gauge field in 2+1
dimensions, in the presence of moving mirrors: We study the Dynamical Casimir Effect (DCE) due to an Abelian gauge field in
2+1 dimensions, in the presence of semitransparent, zero-width mirrors, which
may move or deform in a time-dependent way. We obtain general expressions for
the probability of motion-induced pair creation, which we render in a more
explicit form, for some relevant states of motion. | General boundary quantum field theory: Foundations and probability
interpretation: We elaborate on the proposed general boundary formulation as an extension of
standard quantum mechanics to arbitrary (or no) backgrounds. Temporal
transition amplitudes are generalized to amplitudes for arbitrary spacetime
regions. State spaces are associated to general (not necessarily spacelike)
hypersurfaces. We give a detailed foundational exposition of this approach,
including its probability interpretation and a list of core axioms. We explain
how standard quantum mechanics arises as a special case. We include a
discussion of probability conservation and unitarity, showing how these
concepts are generalized in the present framework. We formulate vacuum axioms
and incorporate spacetime symmetries into the framework. We show how the
Schroedinger-Feynman approach is a suitable starting point for casting quantum
field theories into the general boundary form. We discuss the role of
operators. |
Quark scattering amplitudes at strong coupling: Following Alday and Maldacena, we describe a string theory method to compute
the strong coupling behavior of the scattering amplitudes of quarks and gluons
in planar N=2 super Yang-Mills theory in the probe approximation. Explicit
predictions for these quantities can be constructed using the all-orders planar
gluon scattering amplitudes of N=4 super Yang-Mills due to Bern, Dixon and
Smirnov. | Extended supersymmetry with gauged central charge: Global N=2 supersymmetry in four dimensions with a gauged central charge is
formulated in superspace. To find an irreducible representation of
supersymmetry for the gauge connections a set of constraints is given. Then the
Bianchi identities are solved subject to this set of constraints. It is shown
that the gauge connection of the central charge is a N=2 vector multiplet.
Moreover the Bogomol'nyi bound of the massive particle states is studied. |
N=2 Super - $W_{3}$ Algebra and N=2 Super Boussinesq Equations: We study classical $N=2$ super-$W_3$ algebra and its interplay with $N=2$
supersymmetric extensions of the Boussinesq equation in the framework of the
nonlinear realization method and the inverse Higgs - covariant reduction
approach. These techniques have been previously applied by us in the bosonic
$W_3$ case to give a new geometric interpretation of the Boussinesq hierarchy.
Here we deduce the most general $N=2$ super Boussinesq equation and two kinds
of the modified $N=2$ super Boussinesq equations, as well as the super Miura
maps relating these systems to each other, by applying the covariant reduction
to certain coset manifolds of linear $N=2$ super-$W_3^{\infty}$ symmetry
associated with $N=2$ super-$W_3$. We discuss the integrability properties of
the equations obtained and their correspondence with the formulation based on
the notion of the second hamiltonian structure. | Instability of (1+1) de sitter space in the presence of interacting
fields: Instabilities of two dimensional (1+1) de Sitter space induced by interacting
fields are studied. As for the case of flat Minkowski space, several
interacting fermion models can be translated into free boson ones and vice
versa. It is found that interacting fermion theories do not lead to any
instabilities, while the interacting bosonic sine-Gordon model does lead to a
breakdown of de Sitter symmetry and to the vanishing of the vacuum expectation
value of the S matrix. |
Black hole interiors in holographic topological semimetals: We study the black hole interiors in holographic Weyl semimetals and
holographic nodal line semimetals. We find that the black hole singularities
are of Kasner form. In the topologically nontrivial phase at low temperature,
both the Kasner exponents of the metric fields and the proper time from the
horizon to the singularity are almost constant, likely reflecting the
topological nature of the topological semimetals. We also find some specific
behaviors inside the horizon in each holographic semimetal model. | Quantum Fisher information as a probe for Unruh thermality: A long-standing debate on Unruh effect is about its obscure thermal nature.
In this Letter, we use quantum Fisher information (QFI) as an effective probe
to explore the thermal nature of Unruh effect from both local and global
perspectives. By resolving the full dynamics of UDW detector, we find that the
QFI is a time-evolving function of detector's energy gap, Unruh temperature
$T_U$ and particularities of background field, e.g., mass and spacetime
dimensionality. We show that the asymptotic QFI whence detector arrives its
equilibrium is solely determined by $T_U$, demonstrating the global side of
Unruh thermality alluded by the KMS condition. We also show that the local side
of Unruh effect, i.e., the different ways for the detector to approach the same
thermal equilibrium, is encoded in the corresponding time-evolution of the QFI.
In particular, we find that with massless scalar background the QFI has unique
monotonicity in $n=3$ dimensional spacetime, and becomes non-monotonous for
$n\neq3$ models where a local peak value exists at early time and for finite
acceleration, indicating an enhanced precision of estimation on Unruh
temperature at a relative low acceleration can be achieved. Once the field
acquiring mass, the related QFI becomes significantly robust against the Unruh
decoherence in the sense that its local peak sustains for a very long time.
While coupling to a more massive background, the persistence can even be
strengthened and the QFI possesses a larger maximal value. Such robustness of
QFI can surely facilitate any practical quantum estimation task. |
Charged AdS Black Holes and Catastrophic Holography: We compute the properties of a class of charged black holes in anti-de Sitter
space-time, in diverse dimensions. These black holes are solutions of
consistent Einstein-Maxwell truncations of gauged supergravities, which are
shown to arise from the inclusion of rotation in the transverse space. We
uncover rich thermodynamic phase structures for these systems, which display
classic critical phenomena, including structures isomorphic to the van der
Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the
universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All
of the thermodynamics is consistent with field theory interpretations via
holography, where the dual field theories can sometimes be found on the world
volumes of coincident rotating branes. | Conformal symmetry and nonlinear extensions of nonlocal gravity: We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity
theory. We extend this theory in two different ways suggested by conformal
symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the
operator that enters the action for a conformally-coupled scalar field, or
replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a
four-derivative operator that enters in the effective action induced by the
conformal anomaly. We show that the former modification gives an interesting
and viable cosmological model, with a dark energy equation of state today
$w_{\rm DE}\simeq -1.01$, which very closely mimics $\Lambda$CDM and evolves
asymptotically into a de Sitter solution. The model based on the Paneitz
operator seems instead excluded by the comparison with observations. We also
review some issues about the causality of nonlocal theories, and we point out
that these nonlocal models can be modified so to nicely interpolate between
Starobinski inflation in the primordial universe and accelerated expansion in
the recent epoch. |
Thermal Field Theory and Infinite Statistics: We construct a quantum thermal field theory for scalar particles in the case
of infinite statistics. The extension is provided by working out the Fock space
realization of a "quantum algebra", and by identifying the hamiltonian as the
energy operator. We examine the perturbative behavior of this theory and in
particular the possible extension of the KLN theorem, and argue that it appears
as a stable structure in a quantum field theory context. | Horizon Acoustics of the GHS Black Hole and the Spectrum of ${\rm
AdS}_2$: We uncover a novel structure in Einstein-Maxwell-dilaton gravity: an ${\rm
AdS}_2 \times S^2$ solution in string frame, which can be obtained by a
near-horizon limit of the extreme GHS black hole with dilaton coupling $\lambda
\neq 1$. Unlike the Bertotti-Robinson spacetime, our solution has independent
length scales for the ${\rm AdS}_2$ and $S^2$, with ratio controlled by
$\lambda$. We solve the perturbation problem for this solution, finding the
independently propagating towers of states in terms of superpositions of
gravitons, photons, and dilatons and their associated effective potentials.
These potentials describe modes obeying conformal quantum mechanics, with
couplings that we compute, and can be recast as giving the spectrum of the
effective masses of the modes. By dictating the conformal weights of boundary
operators, this spectrum provides crucial data for any future construction of a
holographic dual to these ${\rm AdS}_2\times S^2$ configurations. |
Strong coupling expansion of free energy and BPS Wilson loop in
$\mathcal N=2$ superconformal models with fundamental hypermultiplets: As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of
strong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4d
superconformal models we consider two special theories with gauge groups
$SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets
in rank 2 antisymmetric and fundamental representations and are
planar-equivalent to the corresponding $\mathcal N=4$ SYM theories. These
$\mathcal N=2$ theories can be realised on a system of $N$ D3-branes with a
finite number of D7-branes and O7-plane; the dual string theories should be
particular orientifolds of $AdS_5\times S^5$ superstring. Starting with the
localization matrix model representation for the $\mathcal N=2$ partition
function on $S^4$ we find exact differential relations between the $1/N$ terms
in the corresponding free energy $F$ and the $\frac{1}{2}$-BPS Wilson loop
expectation value $\langle\mathcal W\rangle$ and also compute their large 't
Hooft coupling ($\lambda \gg 1$) expansions. The structure of these expansions
is different from the previously studied models without fundamental
hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed
expression for the leading strong coupling terms at each order in the $1/N$
expansion. We also determine the exponentially suppressed at large $\lambda$
contributions to the non-planar corrections to $F$ and $\langle\mathcal
W\rangle$ and comment on their resurgence properties. We discuss dual string
theory interpretation of these strong coupling expansions. | Type IIB Flows with N=1 Supersymmetry: We write general and explicit equations which solve the supersymmetry
transformations with two arbitrary complex-proportional Weyl spinors on
$\mathcal{N}=1$ supersymmetric type IIB strings backgrounds with all R-R $F_1$,
$F_3$, $F_5$ and NS-NS $H_3$ fluxes turned on using SU(3) structures. The
equations are generalizations of the ones found for specific relations between
the two spinors by Grana, Minasian, Petrini and Tomasiello in [1] and by Butti,
Grana, Minasian, Petrini and Zaffaroni in [2]. The general equations allow to
study systematically generic type IIB backgrounds with $\mathcal{N}=1$
supersymmetry. We then explore some specific classes of flows with constant
axion, flows with constant dilaton, flows on conformally Calabi-Yau
backgrounds, flows with imaginary self-dual 3-form flux, flows with constant
ratio of the two spinors, the corresponding equations are written down and some
of their features and relations are discussed. |
Bulk-Boundary Correspondence in the Quantum Hall Effect: We present a detailed microscopic study of edge excitations for n filled
Landau levels. We show that the higher-level wavefunctions possess a
non-trivial radial dependence that should be integrated over for properly
defining the edge conformal field theory. This analysis let us clarify the role
of the electron orbital spin s in the edge theory and to discuss its
universality, thus providing a further instance of the bulk-boundary
correspondence. We find that the values s_i for each level, i=1,...,n,
parameterize a Casimir effect or chemical potential shift that could be
experimentally observed. These results are generalized to fractional and
hierarchical fillings by exploiting the W-infinity symmetry of incompressible
Hall fluids. | Star--Matrix Models: The star-matrix models are difficult to solve due to the multiple powers of
the Vandermonde determinants in the partition function. We apply to these
models a modified Q-matrix approach and we get results consistent with those
obtained by other methods.As examples we study the inhomogenous gaussian model
on Bethe tree and matrix $q$-Potts-like model. For the last model in the
special cases $q=2$ and $q=3$, we write down explicit formulas which
determinate the critical behaviour of the system.For $q=2$ we argue that the
critical behaviour is indeed that of the Ising model on the $\phi^3$ lattice. |
Trees: An algebraic formalism, developped with V. Glaser and R. Stora for the study
of the generalized retarded functions of quantum field theory, is used to prove
a factorization theorem which provides a complete description of the
generalized retarded functions associated with any tree graph. Integrating over
the variables associated to internal vertices to obtain the perturbative
generalized retarded functions for interacting fields arising from such graphs
is shown to be possible for a large category of space-times. | Derivation of Transport Equations using the Time-Dependent Projection
Operator Method: We develop a formalism to carry out coarse-grainings in quantum field
theoretical systems by using a time-dependent projection operator in the
Heisenberg picture. A systematic perturbative expansion with respect to the
interaction part of the Hamiltonian is given, and a Langevin-type equation
without a time-convolution integral term is obtained. This method is applied to
a quantum field theoretical model, and coupled transport equations are derived. |
All-orders asymptotics of tensor model observables from symmetries of
restricted partitions: The counting of the dimension of the space of $U(N) \times U(N) \times U(N)$
polynomial invariants of a complex $3$-index tensor as a function of degree $n$
is known in terms of a sum of squares of Kronecker coefficients. For $n \le N$,
the formula can be expressed in terms of a sum of symmetry factors of
partitions of $n$ denoted $Z_3(n)$. We derive the large $n$ all-orders
asymptotic formula for $ Z_3(n)$ making contact with high order results
previously obtained numerically. The derivation relies on the dominance in the
sum, of partitions with many parts of length $1$. The dominance of other small
parts in restricted partition sums leads to related asymptotic results. The
result for the $3$-index tensor observables gives the large $n$ asymptotic
expansion for the counting of bipartite ribbon graphs with $n$ edges, and for
the dimension of the associated Kronecker permutation centralizer algebra. We
explain how the different terms in the asymptotics are associated with
probability distributions over ribbon graphs. The large $n$ dominance of small
parts also leads to conjectured formulae for the asymptotics of invariants for
general $d$-index tensors. The coefficients of $ 1/n$ in these expansions
involve Stirling numbers of the second kind along with restricted partition
sums. | Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic
M-theory Satisfying Swampland Conjectures: We recently described a protocol for computing the potential energy in
heterotic M-theory for the dilaton, complex structure and K\"ahler moduli. This
included the leading order non-perturbative contributions to the complex
structure, gaugino condensation and worldsheet instantons assuming a hidden
sector that contains an anomalous U(1) structure group embedded in $E_8$. In
this paper, we elucidate, in detail, the mathematical and computational methods
required to utilize this protocol. These methods are then applied to a
realistic heterotic M-theory model, the $B-L$ MSSM, whose observable sector is
consistent with all particle physics requirements. Within this context, it is
shown that the dilaton and universal moduli can be completely stabilized at
values compatible with every phenomenological and mathematical constraint -- as
well as with $\Lambda$CDM cosmology. We also show that the heterotic M-theory
vacua are consistent with all well-supported Swampland conjectures based on
considerations of string theory and quantum gravity, and we discuss the
implications of dark energy theorems for compactified theories. |
Towards a quadratic Poisson algebra for the subtracted classical
monodromy of Symmetric Space Sine-Gordon theories: Symmetric Space Sine-Gordon theories are two-dimensional massive integrable
field theories, generalising the Sine-Gordon and Complex Sine-Gordon theories.
To study their integrability properties on the real line, it is necessary to
introduce a subtracted monodromy matrix. Moreover, since the theories are not
ultralocal, a regularisation is required to compute the Poisson algebra for the
subtracted monodromy. In this article, we regularise and compute this Poisson
algebra for certain configurations, and show that it can both satisfy the
Jacobi identity and imply the existence of an infinite number of conserved
quantities in involution. | Asymptotic Dynamics of Monopole Walls: We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole
in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs
curve using the Newton polytope and amoeba. In particular, we show that the
monopole wall splits into subwalls when any of its moduli become large. The
long-distance gauge and Higgs field interactions of these subwalls are abelian,
allowing us to derive an asymptotic metric for the monopole wall moduli space. |
Entropy of Operator-valued Random Variables: A Variational Principle for
Large N Matrix Models: We show that, in 't Hooft's large N limit, matrix models can be formulated as
a classical theory whose equations of motion are the factorized
Schwinger--Dyson equations. We discover an action principle for this classical
theory. This action contains a universal term describing the entropy of the
non-commutative probability distributions. We show that this entropy is a
nontrivial 1-cocycle of the non-commutative analogue of the diffeomorphism
group and derive an explicit formula for it. The action principle allows us to
solve matrix models using novel variational approximation methods; in the
simple cases where comparisons with other methods are possible, we get
reasonable agreement. | Cosmological quantum states of de Sitter-Schwarzschild are static patch
partition functions: We solve the Wheeler-DeWitt equation in the 'cosmological interior' (the past
causal diamond of future infinity) of four dimensional dS-Schwarzschild
spacetimes. Within minisuperspace there is a basis of solutions labelled by a
constant $c$, conjugate to the mass of the black hole. We propose that these
solutions are in correspondence with partition functions of a dual quantum
mechanical theory where $c$ plays the role of time. The quantum mechanical
theory lives on worldtubes in the 'static patch' of dS-Schwarzschild, and the
partition function is obtained by evolving the corresponding Wheeler-DeWitt
wavefunction through the cosmological horizon, where a metric component
$g_{tt}$ changes sign. We establish that the dual theory admits a symmetry
algebra given by a central extension of the Poincar\'e algebra
$\mathfrak{e}(1,1)$ and that the entropy of the dS black hole is encoded as an
averaging of the dual partition function over the background $g_{tt}$. |
Modularity, Quaternion-Kahler spaces and Mirror Symmetry: We provide an explicit twistorial construction of quaternion-Kahler manifolds
obtained by deformation of c-map spaces and carrying an isometric action of the
modular group SL(2,Z). The deformation is not assumed to preserve any
continuous isometry and therefore this construction presents a general
framework for describing NS5-brane instanton effects in string
compactifications with N=2 supersymmetry. In this context the modular invariant
parametrization of twistor lines found in this work yields the complete
non-perturbative mirror map between type IIA and type IIB physical fields. | BPS preons in supergravity and higher spin theories. An overview from
the hill of twistor appraoch: We review briefly the notion of BPS preons, first introduced in
11-dimensional context as hypothetical constituents of M-theory, in its
generalization to arbitrary dimensions and emphasizing the relation with
twistor approach. In particular, the use of a 'twistor-like' definition of BPS
preon (almost) allows us to remove supersymmetry arguments from the discussion
of the relation of the preons with higher spin theories and also of the
treatment of BPS preons as constituents. We turn to the supersymmetry in the
second part of this contribution, where we complete the algebraic discussion
with supersymmetric arguments based on the M-algebra (generalized Poincare
superalgebra), discuss the possible generalization of BPS preons related to the
osp(1|n) (generalized AdS) superalgebra, review a twistor-like kappa-symmetric
superparticle in tensorial superspace, which provides a point-like dynamical
model for BPS preon, and the role of BPS preons in the analysis of supergravity
solutions. Finally we describe resent results on the concise superfield
description of the higher spin field equations and on superfield supergravity
in tensorial superspaces. |
Analytic bootstrap for magnetic impurities: We study the $O(3)$ critical model and the free theory of a scalar triplet in
the presence of a magnetic impurity. We use analytic bootstrap techniques to
extract results in the $\varepsilon$-expansion. First, we extend by one order
in perturbation theory the computation of the beta function for the defect
coupling in the free theory. Then, we analyze in detail the low-lying spectrum
of defect operators, focusing on their perturbative realization when the defect
is constructed as a path-ordered exponential. After this, we consider two
different bulk two-point functions and we compute them using the defect
dispersion relation. For a free bulk theory, we are able to fix the form of the
correlator at all orders in $\varepsilon$, while for an interacting bulk we
compute it up to second order in $\varepsilon$. Expanding these results in the
bulk and defect block expansions, we are able to extract an infinite set of
defect CFT data. We discuss low-spin ambiguities that affect every result
computed through the dispersion relation and we use a combination of
consistency conditions and explicit diagrammatic calculations to fix this
ambiguity. | Aspects of Defects in 3d-3d Correspondence: In this paper we study supersymmetric co-dimension 2 and 4 defects in the
compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold
$M$. The so-called 3d-3d correspondence is a relation between complexified
Chern-Simons theory (with gauge group $SL(N, \mathbb{C})$) on $M$ and a 3d
$\mathcal{N}=2$ theory $T_{N}[M]$. We establish a dictionary for this
correspondence in the presence of supersymmetric defects, which are knots/links
inside the 3-manifold. Our study employs a number of different methods:
state-integral models for complex Chern-Simons theory, cluster algebra
techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also
supergravity analysis through holography. These methods are complementary and
we find agreement between them. In some cases the results lead to highly
non-trivial predictions on the partition function. Our discussion includes a
general expression for the cluster partition function, in particular for
non-maximal punctures and $N>2$. We also highlight the non-Abelian description
of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its
Higgsing prescription and the resulting `refinement' in complex CS theory. This
paper is a companion to our shorter paper arXiv:1510.03884, which summarizes
our main results. |
Incompressible topological solitons: We discover a new class of topological solitons. These solitons can exist in
a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be
placed in any finite volume, because the resulting formal solutions have
infinite energy. These objects are, therefore, interpreted as totally
incompressible solitons.
As a first, particular example we consider (1+1) dimensional kinks in
theories with a nonstandard kinetic term or, equivalently, in models with the
so-called runaway (or vacummless) potentials. But incompressible solitons exist
also in higher dimensions. As specific examples in (3+1) dimensions we study
Skyrmions in the dielectric extensions both of the minimal and the BPS Skyrme
models. In the the latter case, the skyrmionic matter describes a completely
incompressible topological perfect fluid. | Giant Gravitons - with Strings Attached (I): In this article, the free field theory limit of operators dual to giant
gravitons with open strings attached are studied. We introduce a graphical
notation, which employs Young diagrams, for these operators. The computation of
two point correlation functions is reduced to the application of three simple
rules, written as graphical operations performed on the Young diagram labels of
the operators. Using this technology, we have studied gravitational radiation
by giant gravitons and bound states of giant gravitons, transitions between
excited giant graviton states and joining of open strings attached to the
giant. |
On the Geometry of Supersymmetric Quantum Mechanical Systems: We consider some simple examples of supersymmetric quantum mechanical systems
and explore their possible geometric interpretation with the help of geometric
aspects of real Clifford algebras. This leads to natural extensions of the
considered systems to higher dimensions and more complicated potentials. | Structure of the two-boundary XXZ model with non-diagonal boundary terms: We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations. |
Diagrammatic Expansion of Non-Perturbative Little String Free Energies: In arXiv:1911.08172 we have studied the single-particle free energy of a
class of Little String Theories of A-type, which are engineered by $N$ parallel
M5-branes on a circle. To leading instanton order (from the perspective of the
low energy $U(N)$ gauge theory) and partially also to higher order, a
decomposition was observed, which resembles a Feynman diagrammatic expansion:
external states are given by expansion coefficients of the $N=1$ BPS free
energy and a quasi-Jacobi form that governs the BPS-counting of an M5-brane
coupling to two M2-branes. The effective coupling functions were written as
infinite series and similarities to modular graph functions were remarked. In
the current work we continue and extend this study: Working with the full
non-perturbative BPS free energy, we analyse in detail the cases $N=2,3$ and
$4$. We argue that in these cases to leading instanton order all coupling
functions can be written as a simple combination of two-point functions of a
single free scalar field on the torus. We provide closed form expressions,
which we conjecture to hold for generic $N$. To higher instanton order, we
observe that a decomposition of the free energy in terms of higher point
functions with the same external states is still possible but a priori not
unique. We nevertheless provide evidence that tentative coupling functions are
still combinations of scalar Greens functions, which are decorated with
derivatives or multiplied with holomorphic Eisenstein series. We interpret
these decorations as corrections of the leading order effective couplings and
in particular link the latter to dihedral graph functions with bivalent
vertices, which suggests an interpretation in terms of disconnected graphs. | One Loop Calculations in Gauge Theories Regulated on an $x^+$-$p^+$
Lattice: In earlier work, the planar diagrams of $SU(N_c)$ gauge theory have been
regulated on the light-cone by a scheme involving both discrete $p^+$ and
$\tau=ix^+$. The transverse coordinates remain continuous, but even so all
diagrams are rendered finite by this procedure. In this scheme quartic
interactions are represented as two cubics mediated by short lived fictitious
particles whose detailed behavior could be adjusted to retain properties of the
continuum theory, at least at one loop. Here we use this setup to calculate the
one loop three gauge boson triangle diagram, and so complete the calculation of
diagrams renormalizing the coupling to one loop. In particular, we find that
the cubic vertex is correctly renormalized once the couplings to the fictitious
particles are chosen to keep the gauge bosons massless. |
Geometrical methods in loop calculations and the three-point function: A geometrical way to calculate N-point Feynman diagrams is reviewed. As an
example, the dimensionally-regulated three-point function is considered,
including all orders of its epsilon-expansion. Analytical continuation to other
regions of the kinematical variables is discussed. | AdS/QCD oddball masses and Odderon Regge trajectory from a twist-five
operator approach: In this work, we consider a massive gauge boson field in AdS$_5$ dual to odd
glueball states with twist-5 operator in 4D Minkowski spacetime. Introducing an
IR cutoff we break the conformal symmetry of the boundary theory allowing us to
calculate the glueball masses with odd spins using Dirichlet and Neumann
boundary conditions. Then, from these masses we construct the corresponding
Regge trajectories associated with the odderon. Our results are compatible with
the ones in the literature. |
The Operator Manifold Formalism. I: The suggested operator manifold formalism enables to develop an approach to
the unification of the geometry and the field theory. We also elaborate the
formalism of operator multimanifold yielding the multiworld geometry involving
the spacetime continuum and internal worlds, where the subquarks are defined
implying the Confinement and Gauge principles. This formalism in Part II
(hep-th/9812182) is used to develop further the microscopic approach to some
key problems of particle physics. | Domain walls and M2-branes partition functions: M-theory and ABJM Theory: We study the BPS counting functions (free energies) of the M-string
configurations. We consider separated M5-branes along with M2-branes stretched
between them, with M5-branes acting as domain walls interpolating different
configurations of M2-branes. We find recursive structure in the free energies
of these configurations. The M-string degrees of freedom on the domain walls
are interpreted in terms of a pair of interacting supersymmetric WZW models. We
also compute the elliptic genus of the M-string in a toy model of the ABJM
theory and compare it with the M-theory computation. |
Exotic Courant algebroids and T-duality: In this paper, we extend the T-duality isomorphism by Gualtieri and
Cavalcanti, from invariant exact Courant algebroids, to exotic exact Courant
algebroids such that the momentum and winding numbers are exchanged, filling in
a gap in the literature. | A model for massless higher spin field interacting with a geometrical
background: We study a very general four dimensional Field Theory model describing the
dynamics of a massless higher spin $N$ symmetric tensor field particle
interacting with a geometrical background.This model is invariant under the
action of an extended linear diffeomorphism. We investigate the consistency of
the equations of motion, and the highest spin degrees of freedom are extracted
by means of a set of covariant constraints. Moreover the the highest spin
equations of motions (and in general all the highest spin field 1-PI
irreducible Green functions) are invariant under a chain of transformations
induced by a set of $N-2$ Ward operators, while the auxiliary fields equations
of motion spoil this symmetry. The first steps to a quantum extension of the
model are discussed on the basis of the Algebraic Field Theory.Technical
aspects are reported in Appendices; in particular one of them is devoted to
illustrate the spin-$2$ case. |
Superluminality and UV Completion: The idea that the existence of a consistent UV completion satisfying the
fundamental axioms of local quantum field theory or string theory may impose
positivity constraints on the couplings of the leading irrelevant operators in
a low-energy effective field theory is critically discussed. Violation of these
constraints implies superluminal propagation, in the sense that the
low-frequency limit of the phase velocity $v_{\rm ph}(0)$ exceeds $c$. It is
explained why causality is related not to $v_{\rm ph}(0)$ but to the
high-frequency limit $v_{\rm ph}(\infty)$ and how these are related by the
Kramers-Kronig dispersion relation, depending on the sign of the imaginary part
of the refractive index $\Ima n(\w)$ which is normally assumed positive.
Superluminal propagation and its relation to UV completion is investigated in
detail in three theories: QED in a background electromagnetic field, where the
full dispersion relation for $n(\w)$ is evaluated numerically for the first
time and the role of the null energy condition $T_{\m\n}k^\m k^\n \ge 0$ is
highlighted; QED in a background gravitational field, where examples of
superluminal low-frequency phase velocities arise in violation of the
positivity constraints; and light propagation in coupled laser-atom
$\L$-systems exhibiting Raman gain lines with $\Ima n(\w) < 0$. The possibility
that a negative $\Ima n(\w)$ must occur in quantum field theories involving
gravity to avoid causality violation, and the implications for the relation of
IR effective field theories to their UV completion, are carefully analysed. | Further Evidence for Lattice-Induced Scaling: We continue our study of holographic transport in the presence of a
background lattice. We recently found evidence that the presence of a lattice
induces a new intermediate scaling regime in asymptotically $AdS_4$ spacetimes.
This manifests itself in the optical conductivity which exhibits a robust
power-law dependence on frequency, $\sigma \sim \omega^{-2/3}$, in a
"mid-infrared" regime, a result which is in striking agreement with experiments
on the cuprates. Here we provide further evidence for the existence of this
intermediate scaling regime. We demonstrate similar scaling in the
thermoelectric conductivity, find analogous scalings in asymptotically $AdS_5$
spacetimes, and show that we get the same results with an ionic lattice. |
String Representation of Field Correlators in the SU(3)-Gluodynamics: The string representation of the Abelian projected SU(3)-gluodynamics
partition function is derived by using the path-integral duality
transformation. On this basis, we also derive analogous representations for the
generating functionals of correlators of gluonic field strength tensors and
monopole currents, which are finally applied to the evaluation of the
corresponding bilocal correlators. The large distance asymptotic behaviours of
the latter turn out to be in a good agreement with existing lattice data and
the Stochastic Model of the QCD vacuum. | Supergravity description of field theories on curved manifolds and a no
go theorem: In the first part of this paper we find supergravity solutions corresponding
to branes on worldvolumes of the form $R^d \times \Sigma$ where $\Sigma$ is a
Riemann surface. These theories arise when we wrap branes on holomorphic
Riemann surfaces inside $K3$ or CY manifolds. In some cases the theory at low
energies is a conformal field theory with two less dimensions. We find some
non-singular supersymmetric compactifications of M-theory down to $AdS_5$. We
also propose a criterion for permissible singularities in supergravity
solutions.
In the second part of this paper, which can be read independently of the
first, we show that there are no non-singular Randall-Sundrum or de-Sitter
compactifications for large class of gravity theories. |
Dilaton Stabilization in Three-generation Heterotic String Model: We study dilaton stabilization in heterotic string models. By utilizing the
asymmetric orbifold construction, we construct an explicit three-generation
model whose matter content in the visible sector is the supersymmetric standard
model with additional vectorlike matter. This model does not contain any
geometric moduli fields except the dilaton field. Model building at a symmetry
enhancement point in moduli space enlarges the rank of the hidden gauge group.
By analyzing multiple hidden gauge sectors, the dilaton field is stabilized by
the racetrack mechanism. We also discuss a supersymmetry breaking scenario and
F-term uplifting. | QCD With A Chemical Potential, Topology, And The 't Hooft 1/N Expansion: We discuss the dependence of observables on the chemical potential in 't
Hooft's large-N QCD. To this end we use the worldline formalism to expand the
fermionic determinant in powers of 1/N. We consider the hadronic as well as the
deconfining phase of the theory. We discuss the origin of the sign problem in
the worldline approach and elaborate on the planar equivalence between QCD with
a baryon chemical potential and QCD with an isospin chemical potential. We show
that for C-even observables the sign problem occurs at a subleading order in
the 1/N expansion of the fermionic determinant. Finally, we comment on the
finite N theory. |
Simple non-perturbative resummation schemes beyond mean-field: case
study for scalar $φ^4$ theory in 1+1 dimensions: I present a sequence of non-perturbative approximate solutions for scalar
$\phi^4$ theory for arbitrary interaction strength, which contains, but allows
to systematically improve on, the familiar mean-field approximation. This
sequence of approximate solutions is apparently well-behaved and numerically
simple to calculate since it only requires the evaluation of (nested) one-loop
integrals. To test this resummation scheme, the case of $\phi^4$ theory in 1+1
dimensions is considered, finding approximate agreement with known results for
the vacuum energy and mass gap up to the critical point. Because it can be
generalized to other dimensions, fermionic fields and finite temperature, the
resummation scheme could potentially become a useful tool for calculating
non-perturbative properties approximately in certain quantum field theories. | Dimer piling problems and interacting field theory: The dimer tiling problem asks in how many ways can the edges of a graph be
covered by dimers so that each site is covered once. In the special case of a
planar graph, this problem has a solution in terms of a free fermionic field
theory. We rediscover and explore an expression for the number of coverings of
an arbitrary graph by arbitrary objects in terms of an interacting fermionic
field theory first proposed by Samuel. Generalizations of the dimer tiling
problem, which we call `dimer piling problems,' demand that each site be
covered N times by indistinguishable dimers. Our field theory provides a
solution of these problems in the large-N limit. We give a similar path
integral representation for certain lattice coloring problems. |
Blowups in BPS/CFT correspondence, and Painlevé VI: We study four dimensional supersymmetric gauge theory in the presence of
surface and point-like defects (blowups) and propose an identity relating
partition functions at different values of $\Omega$-deformation parameters
$({\varepsilon}_{1}, {\varepsilon}_{2})$. As a consequence, we obtain the
formula conjectured in 2012 by O.Gamayun, N.Iorgov, and O.Lysovyy, relating the
tau-function ${\tau}_{PVI}$ to $c=1$ conformal blocks of Liouville theory and
propose its generalization for the case of Garnier-Schlesinger system. To this
end we clarify the notion of the quasiclassical tau-function ${\tau}_{PVI}$ of
Painlev\'e VI and its generalizations. We also make some remarks about the
sphere partition functions, the boundary operator product expansion in the
${\mathcal{N}}=(4,4)$ sigma models related to four dimensional
${\mathcal{N}}=2$ theories on toric manifolds, discuss crossed instantons on
conifolds, elucidate some aspects of the BPZ/KZ correspondence, and
applications to quantization. | Exact Solution of Long-Range Interacting Spin Chains with Boundaries: We consider integrable models of the Haldane-Shastry type with open boundary
conditions. We define monodromy matrices, obeying the reflection equation,
which generate the symmetries of these models. Using a map to the
Calogero-Sutherland Hamiltonian of BC type, we derive the spectrum and the
highest weight eigenstates. |
A Vanishingly Small Vector Mass from Anisotropy of Higher Dimensional
Spacetime: We consider five-dimensional massive vector-gravity theory which is based on
the foliation preserving diffeomorphism and anisotropic conformal invariance.
It does not have an intrinsic scale and the only relevant parameter is the
anisotropic factor $z$ which characterizes the degree of anisotropy between the
four-dimensional spacetime and the extra dimension. We assume that physical
scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking
of vacuum solution. It is demonstrated that a very small mass for the vector
particle compared to $M_*$ can be achieved with a relatively mild adjustment of
the parameter $z$. At the same time, it is also observed that the motion along
the extra dimension can be highly suppressed and the five-dimensional theory
can be effectively reduced to four-dimensional spacetime. | Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor
Convolutions: A definition of a convolution of tensor fields on group manifolds is given,
which is then generalised to generic homogeneous spaces. This is applied to the
product of gauge fields in the context of `gravity $=$ gauge $\times$ gauge'.
In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST)
gauge transformations of two Yang-Mills gauge fields generate the linear BRST
diffeomorphism transformations of the graviton. This facilitates the definition
of the `gauge $\times$ gauge' convolution product on, for example, the static
Einstein universe, and more generally for ultrastatic spacetimes with compact
spatial slices. |
Matrix $φ^4$ Models on the Fuzzy Sphere and their Continuum Limits: We demonstrate that the UV/IR mixing problems found recently for a scalar
$\phi^4$ theory on the fuzzy sphere are localized to tadpole diagrams and can
be overcome by a suitable modification of the action. This modification is
equivalent to normal ordering the $\phi^4$ vertex. In the limit of the
commutative sphere, the perturbation theory of this modified action matches
that of the commutative theory. | Branes, Black Holes and Topological Strings on Toric Calabi-Yau
Manifolds: We develop means of computing exact degerenacies of BPS black holes on toric
Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping
ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of
P^1's. As explicit examples we consider local P^2, P^1 x P^1 and A_k type ALE
space times C. At large N the D-brane partition function factorizes as a sum
over squares of chiral blocks, the leading one of which is the topological
closed string amplitude on the Calabi-Yau. This is in complete agreement with
the recent conjecture of Ooguri, Strominger and Vafa. |
A new kind of McKay correspondence from non-Abelian gauge theories: The boundary chiral ring of a 2d gauged linear sigma model on a K\"ahler
manifold $X$ classifies the topological D-brane sectors and the massless open
strings between them. While it is determined at small volume by simple group
theory, its continuation to generic volume provides highly non-trivial
information about the $D$-branes on $X$, related to the derived category
$D^\flat(X)$. We use this correspondence to elaborate on an extended notion of
McKay correspondence that captures more general than orbifold singularities. As
an illustration, we work out this new notion of McKay correspondence for a
class of non-compact Calabi-Yau singularities related to Grassmannians. | On thermal field fluctuations in ghost-free theories: We study the response of a scalar thermal field to a $\delta$-probe in the
context of non-local ghost-free theories. In these theories a non-local form
factor is inserted into the kinetic part of the action which does not introduce
new poles. For the case of a static $\delta$-potential we obtain an explicit
expression for the thermal Hadamard function and use it for the calculation of
the thermal fluctuations. We then demonstrate how the presence of non-locality
modifies the amplitude of these fluctuations. Finally, we also discuss the
fluctuation-dissipation theorem in the context of ghost-free quantum field
theories at finite temperature. |
A representation theoretic approach to the WZW Verlinde formula: By exploring the description of chiral blocks in terms of co-invariants, a
derivation of the Verlinde formula for WZW models is obtained which is entirely
based on the representation theory of affine Lie algebras. In contrast to
existing proofs of the Verlinde formula, this approach works universally for
all untwisted affine Lie algebras. As a by-product we obtain a homological
interpretation of the Verlinde multiplicities as Euler characteristics of
complexes built from invariant tensors of finite-dimensional simple Lie
algebras. Our results can also be used to compute certain traces of
automorphisms on the spaces of chiral blocks. Our argument is not rigorous; in
its present form this paper will therefore not be submitted for publication. | Entanglement entropy in a four-dimensional cosmological background: We compute the holographic entanglement entropy of a thermalized CFT on a
time-dependent background in four dimensions. We consider a slab configuration
extending beyond the cosmological horizon of a
Friedmann-Lemaitre-Robertson-Walker metric. We identify a volume term that
corresponds to the thermal entropy of the CFT, as well as terms proportional to
the proper area of the entangling surface which are associated with strongly
entangled degrees of freedom in the vicinity of this surface or with the
expansion. |
Membranes for Topological M-Theory: We formulate a theory of topological membranes on manifolds with G_2
holonomy. The BRST charges of the theories are the superspace Killing vectors
(the generators of global supersymmetry) on the background with reduced
holonomy G_2. In the absence of spinning formulations of supermembranes, the
starting point is an N=2 target space supersymmetric membrane in seven
euclidean dimensions. The reduction of the holonomy group implies a twisting of
the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations
in the normal bundle, in contrast to the ordinary spinning formulation of
topological strings, where twisting is performed with internal U(1) currents of
the N=(2,2) superconformal algebra. The double dimensional reduction on a
circle of the topological membrane gives the strings of the topological A-model
(a by-product of this reduction is a Green-Schwarz formulation of topological
strings). We conclude that the action is BRST-exact modulo topological terms
and fermionic equations of motion. We discuss the role of topological membranes
in topological M-theory and the relation of our work to recent work by Hitchin
and by Dijkgraaf et al. | On Regular Black Holes at Finite Temperature: The Thermo Field Dynamics (TFD) formalism is used to investigate the regular
black holes at finite temperature. Using the Teleparalelism Equivalent to
General Relativity (TEGR) the gravitational Stefan-Boltzmann law and the
gravitational Casimir effect at zero and finite temperature are calculated. In
addition, the first law of thermodynamics is considered. Then the gravitational
entropy and the temperature of the event horizon of a class of regular black
holes are determined. |
Functional RG flow equation: regularization and coarse-graining in phase
space: Starting from the basic path integral in phase space we reconsider the
functional approach to the RG flow of the one particle irreducible effective
average action. On employing a balanced coarse-graining procedure for the
canonical variables we obtain a functional integral with a non trivial measure
which leads to a modified flow equation. We first address quantum mechanics for
boson and fermion degrees of freedom and we then extend the construction to
quantum field theories. For this modified flow equation we discuss the
reconstruction of the bare action and the implications on the computation of
the vacuum energy density. | Matrix Models, Large N Limits and Noncommutative Solitons: A survey of the interrelationships between matrix models and field theories
on the noncommutative torus is presented. The discretization of noncommutative
gauge theory by twisted reduced models is described along with a rigorous
definition of the large N continuum limit. The regularization of arbitrary
noncommutative field theories by means of matrix quantum mechanics and its
connection to noncommutative solitons is also discussed. |
The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories: We clarify the mass dependence of the effective prepotential in N=2
supersymmetric SU(N_c) gauge theories with an arbitrary number N_f<2N_c of
flavors. The resulting differential equation for the prepotential extends the
equations obtained previously for SU(2) and for zero masses. It can be viewed
as an exact renormalization group equation for the prepotential, with the beta
function given by a modular form. We derive an explicit formula for this
modular form when N_f=0, and verify the equation to 2-instanton order in the
weak-coupling regime for arbitrary N_f and N_c. | The connection between nonzero density and spontaneous symmetry breaking
for interacting scalars: We consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero
temperature. At nonzero charge densities, the ground state of these systems is
usually assumed to be a superfluid phase, in which the global symmetry is
spontaneously broken along with Lorentz boosts and time translations. We show
that, in $d>2$ spacetime dimensions, this expectation is always realized at one
loop for arbitrary non-derivative interactions, confirming that the physically
distinct phenomena of nonzero charge density and spontaneous symmetry breaking
occur simultaneously in these systems. We quantify this result by deriving
universal scaling relations for the symmetry breaking scale as a function of
the charge density, at low and high density. Moreover, we show that the
critical value of $\mu$ above which a nonzero density develops coincides with
the pole mass in the unbroken, Poincar\'e invariant vacuum of the theory. The
same conclusions hold non-perturbatively for an ${\rm O}(N)$ theory with
quartic interactions in $d=3$ and $4$, at leading order in the $1/N$ expansion.
We derive these results by computing analytically the zero-temperature,
finite-$\mu$ one-loop effective potential. We check our results against the
one-loop low-energy effective action for the superfluid phonons in $\lambda
\phi^4$ theory in $d=4$ previously derived by Joyce and ourselves, which we
further generalize to arbitrary potential interactions and arbitrary
dimensions. As a byproduct, we find analytically the one-loop scaling dimension
of the lightest charge-$n$ operator for the $\lambda \phi^6$ conformal
superfluid in $d=3$, at leading order in $1/n$, reproducing a numerical result
of Badel et al. For a $\lambda \phi^4$ superfluid in $d=4$, we also reproduce
the Lee--Huang--Yang relation and compute relativistic corrections to it.
Finally, we discuss possible extensions of our results beyond perturbation
theory. |
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