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Superconformal duality-invariant models and $\mathcal{N} = 4$ SYM
effective action: We present $\mathcal{N}=2$ superconformal $\mathsf{U}(1)$ duality-invariant
models for an Abelian vector multiplet coupled to conformal supergravity. In a
Minkowski background, such a nonlinear theory is expected to describe (the
planar part of) the low-energy effective action for the $\mathcal{N}=4$
$\mathsf{SU}(N)$ super-Yang-Mills (SYM) theory on its Coulomb branch where (i)
the gauge group $\mathsf{SU}(N)$ is spontaneously broken to $\mathsf{SU}(N-1)
\times \mathsf{U}(1)$; and (ii) the dynamics is captured by a single
$\mathcal{N}=2$ vector multiplet associated with the $\mathsf{U}(1)$ factor of
the unbroken group. Additionally, a local $\mathsf{U}(1)$ duality-invariant
action generating the $\mathcal{N}=2$ super-Weyl anomaly is proposed. By
providing a new derivation of the recently constructed $\mathsf{U}(1)$
duality-invariant $\mathcal{N}=1$ superconformal electrodynamics, we introduce
its $\mathsf{SL}(2,{\mathbb R})$ duality-invariant coupling to the
dilaton-axion multiplet. | On K3-Thurston 7-manifolds and their deformation space: A case study
with remarks on general K3T and M-theory compactification: M-theory suggests the study of 11-dimensional space-times compactified on
some 7-manifolds. From its intimate relation to superstrings, one possible
class of such 7-manifolds are those that have Calabi-Yau threefolds as
boundary. In this article, we construct a special class of such 7-manifolds,
named as {\it K3-Thurston} (K3T) 7-manifolds. The factor from the K3 part of
the deformation space of these K3T 7-manifolds admits a K\"{a}hler structure,
while the factor of the deformation space from the Thurston part admits a
special K\"{a}hler structure. The latter rings with the nature of the scalar
manifold of a vector multiplet in an N=2 $d=4$ supersymmetric gauge theory.
Remarks and examples on more general K3T 7-manifolds and issues to possible
interfaces of K3T to M-theory are also discussed. |
TASI Lectures on Matrix Theory: This is a summary of key issues in Matrix Theory and its compactifications.
It is emphasized that Matrix Theory is a valid Discrete Light Cone Quantization
of M Theory with at least 6 noncompact asymptotically flat dimensions and 16 or
32 Supersymmetry Charges. The background dependence of the quantum mechanics of
M Theory, and the necessity of working in light cone frame in asymptotically
flat spacetimes are explained in terms of the asymptotic density of states of
the theory, which follows from the Bekenstein-Hawking entropy formula. In four
noncompact dimensions one is led to expect a Hagedorn spectrum in light cone
energy. This suggests the possible relevance of ``little string theories''
(LSTs) to the quantum description of four dimensional compactifications,
because one can argue that their exact high energy spectrum has the Hagedorn
form. Some space is therefore devoted to a discussion of the properties of
LSTs, which were first discovered as the proper formulation of Matrix Theory on
the five torus. | Nonperturbative approach to Yang-Mills thermodynamics: An analytical and nonperturbative approach to SU(2) and SU(3) Yang-Mills
thermodynamics is developed and applied. Each theory comes in three phases: A
deconfining, a preconfining, and a confining one. We show how macroscopic and
inert scalar fields form in each phase and how they determine the ground-state
physics and the properties of the excitations. While the excitations in the
deconfining and preconfining phase are massless or massive gauge modes the
excitations in the confining phase are massless or massive spin-1/2 fermions.
The nature of the two phase transitions is investigated for each theory. We
compute the temperature evolution of thermodynamical quantities in the
deconfining and preconfining phase and estimate the density of states in the
confining phase. Some implications for particle physics and cosmology are
discussed. |
New Symmetries of Massless QED: An infinite number of physically nontrivial symmetries are found for abelian
gauge theories with massless charged particles. They are generated by large
$U(1)$ gauge transformations that asymptotically approach an arbitrary function
$\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity
($\mathscr I^+$) but are independent of the retarded time. The value of
$\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on
$\mathscr I^+$ by the condition that it take the same value at either end of
any light ray crossing Minkowski space. The $\varepsilon\neq$ constant
symmetries are spontaneously broken in the usual vacuum. The associated
Goldstone modes are zero-momentum photons and comprise a $U(1)$ boson living on
the conformal sphere. The Ward identity associated with this asymptotic
symmetry is shown to be the abelian soft photon theorem. | Spherical Symmetric Solutions in Hořava-Lifshitz Gravity and their
Properties: Non-projectable Ho\v{r}ava gravity for a spherically symmetric configuration
with $\lambda=1$ exhibits an infinite set of solutions parametrized by a
generic function $g^{2}(r)$ for the radial component of the shift vector. In
the IR limit the infinite set of solutions corresponds to the invariance of
General Relativity under a spacetime reparametrization. In general, not being a
coordinate transformation, the symmetry in the action responsible for the
infinite set of solutions does not have a clear physical interpretation. Indeed
it is broken by the matter term in the action. We study the behavior of the
solutions for generic values of the parameter $g^{2}(r)$. |
String theory duals of Lifshitz-Chern-Simons gauge theories: We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz
Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These
are nonrelativistic gauge theories in 2+1 dimensions in which parity and
time-reversal symmetries are explicitly broken by the presence of a
Chern-Simons term. We show that these field theories can be realized as
deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic
dictionary, we identify the bulk fields that are dual to these deformations.
The geometries describing the groundstates of the non-Abelian LCS gauge
theories realized here exhibit a mass gap. | RG flows from WZW models: We constrain renormalization group flows from $ABCDE$ type Wess-Zumino-Witten
models triggered by adjoint primaries. We propose positive Lagrangian coupling
leads to massless flow and negative to massive. In the conformal phase, we
prove an interface with the half-integral condition obeys the double braiding
relations. Distinguishing simple and non-simple flows, we conjecture the former
satisfies the half-integral condition. If the conjecture is true, some
previously allowed massless flows are ruled out. For $A$ type, known mixed
anomalies fix the ambiguity in identifications of Verlinde lines; an object is
identified with its charge conjugate. In the massive phase, we compute ground
state degeneracies. |
Asymptotic solvability of an imaginary cubic oscillator with spikes: For the PT symmetric potential of Dorey, Dunning and Tateo we show that in
the large angular momentum (i.e., strongly spiked) limit the low-lying
eigenstates of this popular non-Hermitian problem coincide with the shifted
Hermitian harmonic oscillators calculated at the zero angular momentum. This
type of an approximate Hermitization is valid in all the domain where the
spectrum of energies remains real. It proves very efficient numerically. The
construction is asymmetric with respect to the sign of the subdominant
square-root spike, and exhibits a discontinuity at the point where the PT
symmetric regularization vanishes. | The Shape of Gravity: In a nontrivial background geometry with extra dimensions, gravitational
effects will depend on the shape of the Kaluza-Klein excitations of the
graviton. We investigate a consistent scenario of this type with two positive
tension three-branes separated in a five-dimensional Anti-de Sitter geometry.
The graviton is localized on the ``Planck'' brane, while a gapless continuum of
additional gravity eigenmodes probe the {\it infinitely} large fifth dimension.
Despite the background five-dimensional geometry, an observer confined to
either brane sees gravity as essentially four-dimensional up to a
position-dependent strong coupling scale, no matter where the brane is located.
We apply this scenario to generate the TeV scale as a hierarchically suppressed
mass scale. Arbitrarily light gravitational modes appear in this scenario, but
with suppressed couplings. Real emission of these modes is observable at future
colliders; the effects are similar to those produced by {\it six} large
toroidal dimensions. |
Disordered vector models: from higher spins to incipient strings: We present a one-parameter family of large $N$ disordered models, with and
without supersymmetry, in three spacetime dimensions. They interpolate from the
critical large $N$ vector model dual to a classical higher spin theory, towards
a theory with a classical string dual. We analyze the spectrum and OPE data of
the theories. While the supersymmetric model is always well-behaved the
non-supersymmetric model is unitary only over a small parameter range. We offer
some speculations on the origin of strings from the higher spins. | Rejuvenating the hope of a swampland consistent inflated multiverse with
tachyonic inflation in the high energy RS-II Braneworld: The swampland conjectures from string theory have had some really interesting
implications on cosmology, in particular on inflationary models. Some models of
inflation have been shown to be incompatible with these criterion while some
have been shown to be severely fine tuned, with most of these problems arising
in single field inflationary models in a General relativistic cosmology. Recent
works have although optimistically shown that single field models in more
general cosmologies can be consistent with these conjectures and hence there is
an optimism that not all such models lie in the swampland. However a paradigm
of inflation which has been shown to not be perfectly okay with the conjectures
is eternal inflation. So in this work, we discuss Tachyonic inflation in the
high energy RS-II Braneworld scenario in the context of the swampland
conjectures while also considering the possibility of swampland consistent
eternal inflation. We show that our concerned regime evades all the prominent
swampland issues for single field inflation being virtually unscathed. After
this, we show that the main conflicts of eternal inflation with the swampland
can easily be resolved in the considered tachyonic scenario and in particular,
we also discuss the exciting prospect of a Generalized Uncertainty Principle
facilitating the notion of Swampland consistent eternal inflation. Our work as
a whole reignites the possibility that there can be a swampland (and possibly,
quantum gravitationally) consistent picture of a "Multiverse". |
Pseudo-Goldstini in Field Theory: We consider two SUSY-breaking hidden sectors which decouple when their
respective couplings to the visible particles are switched off. In such a
scenario one expects to find two light fermions: the Goldstino and the
pseudo-Goldstino. While the former remains massless in the rigid limit, the
latter becomes massive due to radiative effects which we analyze from several
different points of view. This analysis is greatly facilitated by a version of
the Goldberger-Treiman relation, which allows us to write a universal
non-perturbative formula for the mass. We carry out the analysis in detail in
the context of gauge mediation, where we find that the pseudo-Goldstino mass is
at least around the GeV scale and can be easily at the electroweak range, even
in low scale models. This leads to interesting and unconventional possibilities
in collider physics and it also has potential applications in cosmology. | Counterterms, critical gravity and holography: We consider counterterms for odd dimensional holographic CFTs. These
counterterms are derived by demanding cut-off independence of the CFT partition
function on $S^d$ and $S^1 \times S^{d-1}$. The same choice of counterterms
leads to a cut-off independent Schwarzschild black hole entropy. When treated
as independent actions, these counterterm actions resemble critical theories of
gravity, i.e., higher curvature gravity theories where the additional massive
spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these
are theories where at least one of the central charges associated with the
trace anomaly vanishes. Connections between these theories and logarithmic CFTs
are discussed. For a specific choice of parameters, the theories arising from
counterterms are non-dynamical and resemble a DBI generalization of gravity.
For even dimensional CFTs, analogous counterterms cancel log-independent
cut-off dependence. |
Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM: When the $SU(N)$ ${\cal N} = 4$ super-Yang-Mills (SYM) theory with
complexified gauge coupling $\tau$ is placed on a round four-sphere and
deformed by an ${\cal N} = 2$-preserving mass parameter $m$, its free energy
$F(m, \tau, \bar \tau)$ can be computed exactly using supersymmetric
localization. In this work, we derive a new exact relation between the fourth
derivative $\partial_m^4 F(m, \tau, \bar \tau) \big|_{m=0}$ of the sphere free
energy and the integrated stress-tensor multiplet four-point function in the
$\mathcal{N}=4$ SYM theory. We then apply this exact relation, along with
various other constraints derived in previous work (coming from analytic
bootstrap, the mixed derivative $\partial_\tau \partial_{\bar \tau}
\partial_m^2 F(m, \tau, \bar \tau) \big|_{m=0}$, and type IIB superstring
theory scattering amplitudes) to determine various perturbative terms in the
large $N$ and large 't Hooft coupling $\lambda$ expansion of the ${\cal N} = 4$
SYM correlator at separated points. In particular, we determine the leading
large-$\lambda$ term in the ${\cal N} = 4$ SYM correlation function at order
$1/N^8$. This is three orders beyond the planar limit. | 3-Leibniz bialgebra in $N=6$ Chern-Simons gauge theories, multiple M2 to
D2 branes and vice versa: Constructing M2-brane and its boundary conditions from D2-brane and the
related boundary conditions and vice versa has been possible in our recent work
by using 3-Lie bialgebra for BLG model with N = 8 supersymmetry. This could be
generalized for BL model with N = 6 by the concept of the 3-Leibniz bialgebra.
The 3-Lie bialgebra is an especial case of 3-Leibniz bialgebra, then more
comprehensive information will be obtained in this work. Consequently,
according to the correspondence of these 3-Leibniz bialgebras with Lie
bialgebras, we reduce to D2-brane such that with some restrictions on the gauge
field this D2-brane is related to the bosonic sector of an N = (4,4) WZW model
equipped with one 2-cocycle in its Lie bialgebra structure. Moreover, the
Basu-Harvey equation which is found by considering boundary conditions for BL
model containing Leibniz bialgebra structure is reduced to Nahm equation and
vice versa using this correspondence. |
Non-relativistic Conformal Field Theory in Momentum Space: Non-relativistic conformal field theory describes many-body physics at
unitarity. The correlation functions of the system are fixed by the requirement
of conformal invariance. In this article, we discuss the correlation functions
of scalar operators in non-relativistic conformal field theories in momentum
space. We discuss the solution of conformal Ward identities and express 2,3,
and 4-point functions as a function of energy and momentum. We also express the
3- and 4-point functions in the momentum space as the one-loop and three-loop
Feynman diagram computations, respectively. | Charged Fermions Tunnelling from Kerr-Newman Black Holes: We consider the tunnelling of charged spin-(1/2) fermions from a Kerr-Newman
black hole and demonstrate that the expected Hawking temperature is recovered.
We discuss certain technical subtleties related to the obtention of this
result. |
On Dual Formulation of Gravity: In this paper we consider a possibility to construct dual formulation of
gravity where the main dynamical field is the Lorentz connection
\omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach
is based on the usual dualization procedure which uses first order parent
Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It
turns out that in d=3 dimensions such dual formulation is related with the so
called exotic parity-violating interactions for massless spin-2 particles. | Radiation of scalar modes and the classical double copy: The double copy procedure relates gauge and gravity theories through
color-kinematics replacements and holds for both scattering amplitudes and in
classical contexts. Moreover, it has been shown that there is a web of theories
whose scattering amplitudes are related through operations that exchange color
and kinematic factors. In this paper, we generalize and extend this procedure
by showing that the classical perturbative double copy of pions corresponds to
special Galileons. We consider point-particles coupled to the relevant scalar
fields, and find the leading and next to leading order radiation amplitudes. By
considering couplings motivated by those that would arise from extracting the
longitudinal modes of the gauge and gravity theories, we are able to map the
non-linear sigma model radiation to that of the special Galileon. We also
construct the single copy by mapping the bi-adjoint scalar radiation to the
non-linear sigma model radiation through generalized color-kinematics
replacements. |
Scalar Field Theories On The World Sheet: Cutoff Independent Treatment: Following earlier work on the same topic, we consider once more scalar field
theories on the world sheet parametrized by the light cone coordinates. For
most of the way, we use the same approach as in the previous work, but there is
an important new development. To avoid the light cone singularity at p^{+}=0,
one world sheet coordinate had to be discretized, introducing a cutoff into the
model.In the earlier work, this cutoff could not be removed, making the model
unreliable. In the present article, we show that, by a careful choice of the
mass counter term, both the infrared singularity at p^{+}=0 and the ultraviolet
mass divergences can be simultaneously eliminated. We therefore finally have a
cutoff independent model on a continuously parametrized world sheet. We study
this model in the mean field approximation, and as before, we find solitonic
solutions. Quantizing the solitonic collective coordinates gives rise to a
string like model. However, in contrast to the standard string model, the
trajectories here are not in general linear but curved. | New rigid string instantons in $R^4$: New rigid string instanton equations are derived. Contrary to standard case,
the equations split into three families. Their solutions in $R^4$ are discussed
and explicitly presented in some cases. |
Renormalization group analysis of reggeon field theory: flow equations: Can large distance high energy QCD be described by Reggeon Field Theory as an
effective emergent theory? We start to investigate the issue employing
functional renormalisation group techniques. | First order flow equations for nonextremal black holes in AdS
(super)gravity: We consider electrically charged static nonextremal black holes in
$d$-dimensional Einstein-Maxwell-(A)dS gravity, whose horizon is a generic
Einstein space in $d-2$ dimensions. It is shown that for this system the
Hamilton-Jacobi equation is exactly solvable and admits two branches of
solutions. One of them exhibits a non-simply connected domain of integration
constants and does not reduce to the well-known solution for the $d=4$ BPS
case. The principal functions generate two first order flows that are
analytically different, but support the same general solution. One of the two
sets of flow equations corresponds to those found by L\"u, Pope and
V\'azquez-Poritz in hep-th/0307001 and (for $d=4$ and $\Lambda=0$) by Miller,
Schalm and Weinberg in hep-th/0612308. This clarifies also the reason for the
very existence of first order equations for nonextremal black holes, namely,
they are just the expressions for the conjugate momenta in terms of derivatives
of the principal function in a Hamilton-Jacobi formalism. In the last part of
our paper we analyze how much of these integrability properties generalizes to
matter-coupled $N=2$, $d=4$ gauged supergravity. |
Causality in Dense Matter: The possibility of non-causal signal propagation is examined for various
theories of dense matter. This investigation requires a discussion of
definitions of causality, together with interpretations of spacetime position.
Specific examples are used to illustrate the satisfaction or violation of
causality in realistic calculations. | The group theory of oxidation II: Cosets of non-split groups: The oxidation program of hep-th/0210178 is extended to cover oxidation of 3-d
sigma model theories on a coset G/H, with G non-compact (but not necessarily
split), and H the maximal compact subgroup. We recover the matter content, the
equations of motion and Bianchi identities from group lattice and Cartan
involution. Satake diagrams provide an elegant tool for the computations, the
maximal oxidation dimension, and group disintegration chains can be directly
read off. We give a complete list of theories that can be recovered from
oxidation of a 3 dimensional coset sigma model on G/H, where G is a simple
non-compact group. |
Alternative conformal quantum mechanics: We investigate a one dimensional quantum mechanical model, which is invariant
under translations and dilations but does not respect the conventional
conformal invariance. We describe the possibility of modifying the conventional
conformal transformation such that a scale invariant theory is also invariant
under this new conformal transformation. | On the nullification of threshold amplitudes: The nullification of threshold amplitudes is considered within the
conventional framework of quantum field theory. The relevant Ward identities
for the reduced theory are derived both on path-integral and diagrammatic
levels. They are then used to prove the vanishing of tree-graph threshold
amplitudes. |
A brane in five-dimensional Minkowski space: We discuss the propagation of gravity in five-dimensional Minkowski space in
the presence of a four-dimensional brane. We show that there exists a solution
to the wave equation that leads to a propagator exhibiting four-dimensional
behavior at low energies (long distances) with five-dimensional effects showing
up as corrections at high energies (short distances). We compare our results
with propagators derived in previous analyses exhibiting five-dimensional
behavior at low energies. We show that different solutions correspond to
different physical systems. | Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement: It is proposed that an event that constitutes a quantum measurement
corresponds to the spontaneous breaking of a symmetry in the measuring device
over time. |
A New Solution to the Callan Rubakov Effect: In this paper we study the scattering of massive fermions off of smooth,
spherically symmetric monopoles in $4d$ $SU(2)$ gauge theory. We propose a
complete physical picture of the monopole-fermion interaction which encompasses
all angular momentum modes. We show that as an in-going fermion scatters off a
monopole, it excites trapped $W$-bosons in the monopole core by a version of
the Witten effect so that the monopole can accrue charge and transform into a
dyon at parametrically low energies. The imparted electric charge is then
protected from decay by an emergent $\mathbb{Z}_N$ generalized global symmetry,
creating a stable dyon. At sufficiently low energies, the scattered fermion can
be trapped by the dyon's electrostatic potential, forming a bound state, which
can decay into spherically symmetric fermion modes subject to the preserved
$\mathbb{Z}_N$ global symmetry. We propose that monopole-fermion scattering can
be described in this way without needing to add ``new'' states to the Hilbert
space, thereby eliminating a long standing confusion in the Callan Rubakov
effect. | Rotating Black Holes in Cubic Gravity: Using on-shell amplitude methods, we derive a rotating black hole solution in
a generic theory of Einstein gravity with additional terms cubic in the Riemann
tensor. We give an explicit expression for the metric in Einsteinian Cubic
Gravity (ECG) and low energy effective string theory, which correctly
reproduces the previously discovered solutions in the zero angular-momentum
limit. We show that at first order in the coupling, the classical potential can
be written to all orders in spin as a differential operator acting on the
non-rotating potential, and we comment on the relation to the Janis-Newman
algorithm. Furthermore, we derive the classical impulse and scattering angle
for such a black hole and comment on the phenomenological interest of such
quantities. |
Thermalization and entanglement following a non-relativistic holographic
quench: We develop a holographic model for thermalization following a quench near a
quantum critical point with non-trivial dynamical critical exponent. The
anti-de Sitter Vaidya null collapse geometry is generalized to asymptotically
Lifshitz spacetime. Non-local observables such as two-point functions and
entanglement entropy in this background then provide information about the
length and time scales relevant to thermalization. The propagation of
thermalization exhibits similar "horizon" behavior as has been seen previously
in the conformal case and we give a heuristic argument for why it also appears
here. Finally, analytic upper bounds are obtained for the thermalization rates
of the non-local observables. | Inflationary Constraints on Type IIA String Theory: We prove that inflation is forbidden in the most well understood class of
semi-realistic type IIA string compactifications: Calabi-Yau compactifications
with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at
large volume and small string coupling. With these ingredients, the first
slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both
inflation (including brane/anti-brane inflation) and de Sitter vacua in this
limit. Our proof is based on the dependence of the 4-dimensional potential on
the volume and dilaton moduli in the presence of fluxes and branes. We also
describe broader classes of IIA models which may include cosmologies with
inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as
NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions
used in deriving the no-go theorem. We focus on NS 5-branes and outline how
such ingredients may prove fruitful for cosmology, but we do not provide an
explicit model. We contrast the results of our IIA analysis with the rather
different situation in IIB. |
Spin Connections and Classification of Inequivalent Quantizations: We discuss an extension of the quantization method based on the induced
representation of the canonical group. | Perturbative BF-Yang-Mills theory on noncommutative R^4: A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented
and in this formulation the U(1) Yang-Mills theory on noncommutative
${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization
using BRST symmetry formalism is discussed and Feynman rules are given.
Computations at one-loop order have been performed and their renormalization
studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is
asymptotically free and its UV-behaviour in the computation of the
$\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills
theories. |
More stable dS vacua from S-dual non-geometric fluxes: Stable vacua obtained from isotropic tori compactification might not be fully
stable provided the existence of runaway directions in the Kaehler directions
of anisotropy. By implementing a genetic algorithm we report the existence of
explicit flux configurations leading to stable de Sitter and Anti- de Sitter
vacua, consisting on Type IIB compactifications on a 6-dimensional anisotropic
torus threaded with standard and S-dual invariant non-geometric fluxes in the
presence of orientifold 3-planes. In all dS vacua the masses of the complex
structure moduli are heavier than the Hubble scale suggesting that the
axio-dilaton and Kaeahler moduli are natural candidates for small-field
inflation. In the way, we also report new solutions on isotropic and
semi-isotropic tori compactifications. Finally, we observe that, since all our
solutions are obtained in the absence of solitonic objects, they are good
candidates to be lifted to stable solutions in extended supersymmetric
theories. | On covariant quantization of M0-brane. Spinor moving frame, pure spinor
formalism and hidden symmetries of D=11 supergravity: The covariant quantization of massless D=11 superparticle (M0-brane) in its
twistor-like Lorentz harmonic formulation is used to clarify the origin and
some properties of the Berkovits pure spinor approach to quantum superstring
and to search for hidden symmetries of D=11 supergravity. In the twistor like
Lorentz harmonic formulation, the SO(16) symmetry is seen already at the
classical level. The quantization produces the linearized supergravity
multiplet as 128+128=256 component Majorana spinor of SO(16) and also shows an
indirect argument in favor of the possible E8 symmetry. |
Numerical evaluation of spherical GJMS determinants for even dimensions: The functional determinants of the GJMS scalar operators, P_{2k}, on
even-dimensional spheres are computed via Barnes multiple gamma functions
relying on the numerical availability of the digamma function. For the critical
k=d/2 case, it is necessary to calculate the Stirling moduli. The
multiplicative anomalies are given as odd polynomials in $k$ and it is
emphasised that that the Dirichlet--to--Robin factorisation, P_{2l+1}, gives
the same results as P_{2k} if k=l+1/2.The results are presented as graphs and
show a series of extrema in the effective action as k is varied in the reals.
For odd dimensions these extrema occur at integer k. | Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal
Model: In the N=1 supersymmetric coset model based on (A_{N-1}^{(1)} \oplus
A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k, N), the lowest N=1 higher spin
supercurrent with spins-(5/2, 3), in terms of two independent numerator WZW
currents, is reviewed. By calculating the operator product expansions (OPE)
between this N=1 higher spin supercurrent and itself, the next two N=1 higher
spin supercurrents can be generated with spins-(7/2, 4) and (4, 9/2). These
four currents are polynomials of degree 3, 4, 4, 4 in the first numerator WZW
currents with level k. The complete nonlinear OPE of the lowest N=1 higher spin
supercurrent for general N is obtained. The three-point functions involving two
scalar primaries with one spin-2 current or spin-3 current are calculated in
the large N limit for all values of the 't Hooft coupling. In particular, the
light states that appeared in the case when the second level was fixed by 1 are
no longer light ones because the eigenvalues are finite in the large N limit. |
Mean Field Method Applied To The New World Sheet Field Theory: String
Formation: The present article is based on a previous one, where a second quantized
field theory on the world sheet for summing the planar graphs of phi^3 theory
was developed. In this earlier work, the ground state of the model was
determined using a variational approximation. Here, starting with the same
world sheet theory, we instead use the mean field method to compute the ground
state, and find results in agreement with the variational calculation. Apart
from serving as a check on the variational calculation, the mean field method
enables us to go beyond the ground state to compute the excited states of the
model. The spectrum of these states is that of a string with linear
trajectories, plus a continuum that starts at higher energy. We show that, by
appropriately tuning the parameters of the model, the string spectrum can be
cleanly seperated from the continuum. | Exact solutions in $\mathcal{R}^{2}$ SUGRA: This letter is devoted to show that the bosonic sector of the
$\mathcal{R}^{2}$-SUGRA in four dimensions, constructed with the F-term, admits
a variety of exact and analytic solutions which include, pp- and AdS waves,
asymptotically flat and AdS black holes and wormholes, as well as product
spacetimes. The existence of static black holes and wormholes implies that a
combination involving the Ricci scalar plus the norm of the field strength of
the auxiliary two-form $B_{\mu\nu}$, must be a constant. We focus on this
sector of the theory which has two subsectors depending on whether such a
combination vanishes or not. |
Non-invertible symmetries along 4d RG flows: We explore novel examples of RG flows preserving a non-invertible
self-duality symmetry. Our main focus is on $\mathcal{N}=1$ quadratic
superpotential deformations of 4d $\mathcal{N}=4$ super-Yang-Mills theory with
gauge algebra $\mathfrak{su}(N)$. A theory that can be obtained in this way is
the so-called $\mathcal{N}=1^*$ SYM where all adjoint chiral multiplets have a
mass. Such IR theory exhibits a rich structure of vacua which we thoroughly
examine. Our analysis elucidates the physics of spontaneous breaking of
self-duality symmetry occurring in the degenerate gapped vacua. The
construction can be generalized, taking as UV starting point a theory of class
$\mathcal{S}$, to demonstrate how non-invertible self-duality symmetries exist
in a variety of $\mathcal{N}=1$ SCFTs. We finally apply this understanding to
prove that the conifold theory has a non-invertible self-duality symmetry. | An admissible level $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2
\right)$-model: modular transformations and the Verlinde formula: The modular properties of the simple vertex operator superalgebra associated
to the affine Kac-Moody superalgebra $\widehat{\mathfrak{osp}} \left( 1
\middle\vert 2 \right)$ at level $-\frac{5}{4}$ are investigated. After
classifying the relaxed highest-weight modules over this vertex operator
superalgebra, the characters and supercharacters of the simple weight modules
are computed and their modular transforms are determined. This leads to a
complete list of the Grothendieck fusion rules by way of a continuous
superalgebraic analogue of the Verlinde formula. All Grothendieck fusion
coefficients are observed to be non-negative integers. These results indicate
that the extension to general admissible levels will follow using the same
methodology once the classification of relaxed highest-weight modules is
completed. |
Gravitational Memory in Higher Dimensions: It is shown that there is a universal gravitational memory effect measurable
by inertial detectors in even spacetime dimensions $d\geq 4$. The effect falls
off at large radius $r$ as $r^{3-d}$. Moreover this memory effect sits at one
corner of an infrared triangle with the other two corners occupied by
Weinberg's soft graviton theorem and infinite-dimensional asymptotic
symmetries. | Computation of Yukawa Couplings for Calabi-Yau Hypersurfaces in Weighted
Projective Spaces: Greene, Morrison and Plesser \cite{GMP} have recently suggested a general
method for constructing a mirror map between a $d$-dimensional Calabi-Yau
hypersurface and its mirror partner for $d > 3$. We apply their method to
smooth hypersurfaces in weighted projective spaces and compute the Chern
numbers of holomorphic curves on these hypersurfaces. As anticipated, the
results satisfy nontrivial integrality constraints. These examples differ from
those studied previously in that standard methods of algebraic geometry which
work in the ordinary projective space case for low degree curves are not
generally applicable. In the limited special cases in which they do work we can
get independent predictions, and we find agreement with our results. |
Cosmic Strings Stabilized by Fermion Fluctuations: We provide a thorough exposition of recent results on the quantum
stabilization of cosmic strings. Stabilization occurs through the coupling to a
heavy fermion doublet in a reduced version of the standard model. The study
combines the vacuum polarization energy of fermion zero-point fluctuations and
the binding energy of occupied energy levels, which are of the same order in a
semi-classical expansion. Populating these bound states assigns a charge to the
string. Strings carrying fermion charge become stable if the Higgs and gauge
fields are coupled to a fermion that is less than twice as heavy as the top
quark. The vacuum remains stable in the model, because neutral strings are not
energetically favored. These findings suggest that extraordinarily large
fermion masses or unrealistic couplings are not required to bind a cosmic
string in the standard model. | Semi-classical Approach to Charged Dilatonic Black Hole in Two
Dimensions: We consider exactly solvable semi-classical theory of two dimensional
dilatonic gravity with electromagnetic interactions. As was done in the paper
by Russo, Susskind and Thorlacius, the term which changes the kinetic term is
added to the action. The theory contains massless fermions as matter fields and
there appear the quantum corrections including chiral anomaly. The screening
effect due to the chiral anomaly has a tendency to cloak the singularity. In a
region of the parameter space, the essential behavior of the theory is similar
to that of Callan, Giddings, Harvey and Strominger's dilatonic black hole
theory modified in the paper by Russo, Susskind and Thorlacius and the
singularity formed by the collapsing matter emerges naked. We find, however,
another region of the parameter space where the singularity disappears in a
finite proper time. Furthermore, in the region of the parameter space, there
appears a discontinuity in the metric on the trajectory of the collapsing
matter, which would be a signal of topology change |
Heat kernel expansion for higher order minimal and nonminimal operators: We build a systematic calculational method for the covariant expansion of the
two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal
differential operators of any order. This is the expansion in powers of
dimensional background field objects -- the coefficients of the operator and
the corresponding spacetime and vector bundle curvatures, suitable in
renormalization and effective field theory applications. For minimal operators
whose principal symbol is given by an arbitrary power of the covariant
Laplacian $(-\Box)^M$, $M>1$, this result generalizes the well-known
Schwinger--DeWitt (or Seeley--Gilkey) expansion to the infinite series of
positive and negative fractional powers of the proper time $\tau^{1/M}$,
weighted by the generalized exponential functions of the dimensionless argument
$-\sigma(x,x')/2\tau^{1/M}$ depending on the Synge world function
$\sigma(x,x')$. The coefficients of this series are determined by the chain of
auxiliary differential operators acting on the two-point parallel transport
tensor, which in their turn follow from the solution of special recursive
equations. The derivation of these operators and their recursive equations are
based on the covariant Fourier transform in curved spacetime. The series of
negative fractional powers of $\tau$ vanishes in the coincidence limit $x'=x$,
which makes the proposed method consistent with the heat kernel theory of
Seeley--Gilkey and generalizes it beyond the heat kernel diagonal in the form
of the asymptotic expansion in the domain $\sigma(x,x')\ll\tau^{1/M}$, $\tau\to
0$.$\nabla^a\sigma(x,x')\ll\tau^{1/2M}$, $\tau\to 0$. | Towards a 2d QFT Analog of the SYK Model: We propose a 2D QFT generalization of the Sachdev-Ye-Kitaev model, which we
argue preserves most of its features. The UV limit of the model is described by
$N$ copies of a topological Ising CFT. The full interacting model exhibits
conformal symmetry in the IR and an emergent pseudo-Goldstone mode that arises
from broken reparametrization symmetry. We find that the effective action of
the Goldstone mode matches with the 3D AdS gravity action, viewed as a
functional of the boundary metric. We compute the spectral density and show
that the leading deviation from conformal invariance looks like a $T \bar{T}$
deformation. We comment on the relation between the IR effective action and
Liouville CFT. |
Deformed supergravity with local R-symmetry: Using deformation theory based on BRST cohomology, a supergravity model is
constructed which interpolates through a continuous deformation parameter
between new minimal supergravity with an extra U(1) gauge multiplet and
standard supergravity with local R-symmetry in a formulation with a nonstandard
set of auxiliary fields. The deformation implements an electromagnetic duality
relating the extra U(1) to the R-symmetry. A consistent representative of the
R-anomaly in the model is proposed too. | The equivalence between the operator approach and the path integral
approach for quantum mechanical non-linear sigma models: We give background material and some details of calculations for two recent
papers [1,2] where we derived a path integral representation of the transition
element for supersymmetric and nonsupersymmetric nonlinear sigma models in one
dimension (quantum mechanics). Our approach starts from a Hamiltonian
$H(\hat{x}, \hat{p}, \hat{\psi}, \hat{\psi}^\dagger)$ with a priori operator
ordering. By inserting a finite number of complete sets of $x$ eigenstates, $p$
eigenstates and fermionic coherent states, we obtain the discretized path
integral and the discretized propagators and vertices in closed form. Taking
the continuum limit we read off the Feynman rules and measure of the continuum
theory which differ from those often assumed. In particular, mode
regularization of the continuum theory is shown in an example to give incorrect
results. As a consequence of time-slicing, the action and Feynman rules,
although without any ambiguities, are necessarily noncovariant, but the final
results are covariant if $\hat{H}$ is covariant. All our derivations are exact.
Two loop calculations confirm our results. |
Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic
Compactifications: We describe the first order moduli space of heterotic string theory
compactifications which preserve $N=1$ supersymmetry in four dimensions, that
is, the infinitesimal parameter space of the Strominger system. We establish
that if we promote a connection on $TX$ to a field, the moduli space
corresponds to deformations of a holomorphic structure $\bar D$ on a bundle
$\cal Q$. The bundle $\cal Q$ is constructed as an extension by the cotangent
bundle $T^*X$ of the bundle $E= {\rm End}(V) \oplus {\rm End}(TX) \oplus TX$
with an extension class $\cal H$ which precisely enforces the anomaly
cancelation condition. The deformations corresponding to the bundle $E$ are
simultaneous deformations of the holomorphic structures on the poly-stable
bundles $V$ and $TX$ together with those of the complex structure of $X$. We
discuss the fact that the "moduli" corresponding to ${\rm End}(TX)$ cannot be
physical, but are however needed in our mathematical structure to be able to
enforce the anomaly cancelation condition. In the Appendix we comment on the
choice of connection on $TX$ which has caused some confusion in the community
before. It has been shown by Ivanov and others that this connection should also
satisfy the instanton equations, and we give another proof of this fact. | Limits on extra dimensions in orbifold compactifications of superstrings: Perturbative breaking of supersymmetry in four-dimensional string theories
predict in general the existence of new large dimensions at the TeV scale. Such
dimensions can be consistent with perturbative unification up to the Planck
scale in a class of string models and open the exciting possibility of lowering
a part of the massive string spectrum at energies accessible to future
accelerators. The main signature is the production of Kaluza-Klein excitations
which have a very particular structure, strongly correlated with the
supersymmetry breaking mechanism. We present a model independent analysis of
the physics of these states in the context of orbifold compactifications of the
heterotic superstring. In particular, we compute the limits on the size of
large dimensions used to break supersymmetry. |
Black holes in asymptotically Lifshitz spacetimes with arbitrary
critical exponent: Recently, a class of gravitational backgrounds in 3+1 dimensions have been
proposed as holographic duals to a Lifshitz theory describing critical
phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We numerically
explore black holes in these backgrounds for a range of values of $z$. We find
drastically different behavior for $z>2$ and $z<2$. We find that for $z>2$
($z<2$) the Lifshitz fixed point is repulsive (attractive) when going to larger
radial parameter $r$. For the repulsive $z>2$ backgrounds, we find a continuous
family of black holes satisfying a finite energy condition. However, for $z<2$
we find that the finite energy condition is more restrictive, and we expect
only a discrete set of black hole solutions, unless some unexpected
cancellations occur. For all black holes, we plot temperature $T$ as a function
of horizon radius $r_0$. For $z\lessapprox 1.761$ we find that this curve
develops a negative slope for certain values of $r_0$ possibly indicating a
thermodynamic instability. | Dynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory: We analyse the world-volume theory of multiple Kaluza-Klein monopoles in
string and M-theory by identifying the appropriate zero modes of various
fields. The results are consistent with supersymmetry, and all conjectured
duality symmetries. In particular for M-theory and type IIA string theory, the
low energy dynamics of N Kaluza-Klein monopoles is described by supersymmetric
U(N) gauge theory, and for type IIB string theory, the low energy dynamics is
described by a (2,0) supersymmetric field theory in (5+1) dimensions with N
tensor multiplets and tensionless self-dual strings. It is also argued that for
the Kaluza-Klein monopoles in heterotic string theory, the apparently flat
moduli space gets converted to the moduli space of BPS monopoles in SU(2) gauge
theory when higher derivative corrections to the supergravity equations of
motion are taken into account. |
An Introduction to On-shell Recursion Relations: This article provides an introduction to on-shell recursion relations for
calculations of tree-level amplitudes. Starting with the basics, such as spinor
notations and color decompositions, we expose analytic properties of
gauge-boson amplitudes, BCFW-deformations, the large $z$-behavior of
amplitudes, and on-shell recursion relations of gluons. We discuss further
developments of on-shell recursion relations, including generalization to other
quantum field theories, supersymmetric theories in particular, recursion
relations for off-shell currents, recursion relation with nonzero boundary
contributions, bonus relations, relations for rational parts of one-loop
amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we
present samples of applications, including solutions of split helicity
amplitudes and of N= 4 SYM theories, consequences of consistent conditions
under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ)
relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye (KLT)
relations. | Aspects of Causality and Unitarity and Comments on Vortex-like
Configurations in an Abelian Model with a Lorentz-Breaking Term: The gauge-invariant Chern-Simons-type Lorentz- and CPT-breaking term is here
reassessed and a spin-projector method is adopted to account for the breaking
(vector) parameter. Issues like causality, unitarity, spontaneous
gauge-symmetry breaking and vortex formation are investigated, and consistency
conditions on the external vector are identified. |
Chiral matter and transitions in heterotic string models: In the framework of N=1 supersymmetric string models given by the heterotic
string on an elliptic Calabi-Yau $\pi :Z\ra B$ together with a SU(n) bundle we
compute the chiral matter content of the massless spectrum. For this purpose
the net generation number, i.e. half the third Chern class, is computed from
data related to the heterotic vector bundle in the spectral cover description;
a non-technical introduction to that method is supplied. This invariant is, in
the class of bundles considered, shown to be related to a discrete modulus
which is the heterotic analogue of the $F$-theory four-flux. We consider also
the relevant matter which is supported along certain curves in the base $B$ and
derive the net generation number again from the independent matter-related
computation. We then illustrate these considerations with two applications.
First we show that the construction leads to numerous 3 generation models of
unbroken gauge group $SU(5), SO(10)$ or $E_6$. Secondly we discuss the closely
related issue of the heterotic 5-brane/instanton transition resp. the
F-theoretic 3-brane/instanton transition. The extra chiral matter in these
transitions is related to the Hecke transform of the direct sum of the original
bundle and the dissolved 5-brane along the intersection of their spectral
covers. Finally we point to the corresponding $F$-theory interpretation of
chiral matter from the intersection of 7-branes where the influence of
four-flux on the twisting along the intersection curve plays a crucial role. | Massive minimal subtraction scheme and "partial-$p$" in anisotropic
Lifshitz space(time)s: We introduce the "partial-$p$" operation in a massive Euclidean
$\lambda\phi^{4}$ scalar field theory describing anisotropic Lifshitz critical
behavior. We then develop a minimal subtraction a la
$Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an application
we compute critical exponents diagrammatically using the orthogonal
approximation at least up to two-loop order and show their equivalence with
other renormalization techniques. We discuss possible applications of the
method in other field-theoretic contexts. |
D-strings and F-strings from string loops: Since the background fields of the string low energy action are supposed to
be the long range manifestation of a condensate of strings, the addition of
world sheet actions to the low energy effective action needs some string
theoretic explanation. In this paper we suggest that this may be understood, as
being due to string loop effects. We first present arguments using an equation
due to Tseytlin and then more rigorously in the particular case of type IIB
theory by invoking the Fischler-Susskind effect. The argument provides further
justification for ${\rm SL}(2,Z)$ duality between D-strings and
F(fundamental)-strings. In an appendix we comment on recent attempts to relate
the type IIA membrane to the 11-dimensional membrane. | Finite Size Giant Magnon: The quantization of the giant magnon away from the infinite size limit is
discussed. We argue that this quantization inevitably leads to string theory on
a Z_M-orbifold of S^5. This is shown explicitly and examined in detail in the
near plane-wave limit. |
Orientifolds, RR Torsion, and K-theory: We analyze the role of RR fluxes in orientifold backgrounds from the point of
view of K-theory, and demonstrate some physical implications of describing
these fluxes in K-theory rather than cohomology. In particular, we show that
certain fractional shifts in RR charge quantization due to discrete RR fluxes
are naturally explained in K-theory. We also show that some orientifold
backgrounds, which are considered distinct in the cohomology classification,
become equivalent in the K-theory description, while others become unphysical. | Heat-kernel coefficients of the Laplace operator on the D-dimensional
ball: We present a very quick and powerful method for the calculation of
heat-kernel coefficients. It makes use of rather common ideas, as integral
representations of the spectral sum, Mellin transforms, non-trivial commutation
of series and integrals and skilful analytic continuation of zeta functions on
the complex plane. We apply our method to the case of the heat-kernel expansion
of the Laplace operator on a $D$-dimensional ball with either Dirichlet,
Neumann or, in general, Robin boundary conditions. The final formulas are quite
simple. Using this case as an example, we illustrate in detail our scheme
---which serves for the calculation of an (in principle) arbitrary number of
heat-kernel coefficients in any situation when the basis functions are known.
We provide a complete list of new results for the coefficients
$B_3,...,B_{10}$, corresponding to the $D$-dimensional ball with all the
mentioned boundary conditions and $D=3,4,5$. |
New numerical results and novel effective string predictions for Wilson
loops: We compute the prediction of the Nambu-Goto effective string model for a
rectangular Wilson loop up to three loops. This is done through the use of an
operatorial, first order formulation and of the open string analogues of
boundary states. This result is interesting since there are universality
theorems stating that the predictions up to three loops are common to all
effective string models. To test the effective string prediction, we set up the
Montecarlo evaluation, in the 3d Ising gauge model, of an observable (the ratio
of two Wilson loops with the same perimeter) for which boundary effects are
relatively small. Our simulation attains a level of precision which is
sufficient to test the two-loop correction. The three-loop correction seems to
go in the right direction, but is actually yet beyond the reach of our
simulation, since its effect is comparable with the statistical errors of the
latter. | Supersymmetric Pair Correlation Function of Wilson Loops: We give a path integral derivation of the annulus diagram in a supersymmetric
theory of open and closed strings with Dbranes. We compute the pair correlation
function of Wilson loops in the generic weakly coupled supersymmetric flat
spacetime background with Dbranes. We obtain a -u^4/r^9 potential between heavy
nonrelativistic sources in a supersymmetric gauge theory at short distances. |
Intersecting domain walls in MQCD: We argue that MQCD admits intersecting domain walls that are realized as
Cayley calibrations of the MQCD M5-brane. We discuss various dual realizations
and comment on how branes can realise domain walls in N=1 supersymmetric
theories in D=3. | Moduli Stabilisation versus Chirality for MSSM like Type IIB
Orientifolds: We investigate the general question of implementing a chiral MSSM like
D-brane sector in Type IIB orientifold models with complete moduli
stabilisation via F-terms induced by fluxes and space-time instantons,
respectively gaugino condensates. The prototype examples are the KKLT and the
so-called large volume compactifications. We show that the ansatz of first
stabilising all moduli via F-terms and then introducing the Standard Model
module is misleading, as a chiral sector notoriously influences the structure
of non-perturbative effects and induces a D-term potential. Focusing for
concreteness on the large volume scenario, we work out the geometry of the
swiss-cheese type Calabi-Yau manifold P_[1,3,3,3,5][15]_(3,75) and analyse
whether controllable and phenomenologically acceptable Kaehler moduli
stabilisation can occur by the combination of F- and D-terms. |
A Representation of the Virasoro Algebra via Wigner-Heisenberg Algebraic
Technique to Bosonic Systems: Using the Wigner-Heisenberg algebra for bosonic systems in connection with
oscillators we find a new representation for the Virasoro algebra. | A note on the KP hierarchy: Given the two boson representation of the conformal algebra \hat W_\infty,
the second Hamiltonian structure of the KP hierarchy, I construct a
bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy
appears as a composite of this new and simpler system. The bi-Hamiltonian
structure of the new hierarchy gives naturally all the Hamiltonian structures
of the KP system. |
Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation: Consistent formulations of relativistic viscous hydrodynamics involve short
lived modes, leading to asymptotic rather than convergent gradient expansions.
In this Letter we consider the Mueller-Israel-Stewart theory applied to a
longitudinally expanding quark-gluon plasma system and identify hydrodynamics
as a universal attractor without invoking the gradient expansion. We give
strong evidence for the existence of this attractor and then show that it can
be recovered from the divergent gradient expansion by Borel summation. This
requires careful accounting for the short-lived modes which leads to an
intricate mathematical structure known from the theory of resurgence. | Scale-separated AdS$_4$ vacua of IIA orientifolds and M-theory: We revisit various aspects of AdS$_4$ flux vacua with scale separation in
type II supergravity and M-theory. We show that massless IIA allows both weakly
and strongly coupled solutions for which the classical orientifold backreaction
can be tuned small. This is explicitly verified by computing the backreaction
at leading order in perturbation theory. We give evidence that the strongly
coupled solutions can be lifted to scale-separated and sourceless (but
classically singular) geometries in 11D supergravity. |
Self-dual $CP(2)$ vortex-like solitons in the presence of magnetic
impurities: We investigate the existence of vortex configurations in two gauged-$CP(2)$
models extended via the inclusion of magnetic impurities. In particular, we
consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged
scenarios, separately. We choose a $CP(2)$-field configuration with a null
topological charge not only in the simplest (free) case, but also when coupled
to an Abelian gauge field. The implementation of the
Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models
for such a configuration possess a self-dual structure which looks like those
inherent to the gauged sigma models. Therefore, when the $CP(2)$ field is
coupled to the Maxwell term, the corresponding total energy possesses both a
well-defined Bogomol'nyi bound and a quantized magnetic flux. Further, when the
$CP(2)$ scenario is gauged with the Chern-Simons action, the total electric
charge is verified to be proportional to the quantized magnetic flux. In
addition, the analysis verifies that the magnetic impurity contributes to the
BPS potentials and appears in both the models' BPS equations. Next, we
introduce a Gaussian type impurity and solve the self-dual equations via a
finite-difference scheme. The resulting solutions present a nonmonotonic
behavior that flips both the magnetic and electric fields. Finally, we discuss
the topologically trivial solutions in the limit for which the impurity becomes
a Dirac $\delta $-function. | Restoration and Dynamical Breakdown of the φ\to -φSymmetry in
the (1+1)-dimensional Massive sine-Gordon Field Theory: Within the framework of the Gaussian wave-functional approach, we investigate
the influences of quantum and finite-temperature effects on the
Z_2-symmetry(\phi \to -\phi) of the (1+1)-dimensional massive sine-Gordon field
theory. It is explicitly demonstrated that by quantum effects the Z_2-symmetry
can be restored in one region of the parameter space and dynamically
spontaneously broken in another region. Moreover, a finite-temperature effect
can further restore the Z_2-symmetry only. |
AdS$_4$/CFT$_3$ from Weak to Strong String Coupling: We consider the four-point function of operators in the stress tensor
multiplet of the $U(N)_k\times U(N)_{-k}$ ABJM theory, in the limit where $N$
is taken to infinity while $N/k^{5}$ is held fixed. In this limit, ABJM theory
is holographically dual to type IIA string theory on $AdS_4\times
\mathbb{CP}^3$ at finite string coupling $g_s \sim (N/k^5)^{1/4}$. While at
leading order in $1/N$, the stress tensor multiplet four-point function can be
computed from type IIA supergravity, in this work we focus on the first
subleading correction, which comes from tree level Witten diagrams with an
$R^4$ interaction vertex. Using superconformal Ward identities, bulk locality,
and the mass deformed sphere free energy previously computed to all orders in
$1/N$ from supersymmetric localization, we determine this $R^4$ correction as a
function of $N/k^5$. Taking its flat space limit, we recover the known $R^4$
contribution to the type IIA S-matrix and reproduce the fact that it only
receives perturbative contributions in $g_s$ from genus zero and genus one
string worldsheets. This is the first check of AdS/CFT at finite $g_s$ for
local operators. Our result for the four-point correlator interpolates between
the large $N$, large 't Hooft coupling limit and the large $N$ finite $k$
limit. From the bulk perspective, this is an interpolation between type IIA
string theory on $AdS_4\times \mathbb{CP}^3$ at small string coupling and
M-theory on $AdS_4\times S^7/\mathbb{Z}_k$. | Divergences in the rate of complexification: It is conjectured that the average energy provides an upper bound on the rate
at which the complexity of a holographic boundary state grows. In this paper,
we perturb a holographic CFT by a relevant operator with a time-dependent
coupling, and study the complexity of the time-dependent state using the
\textit{complexity equals action} and the \textit{complexity equals volume}
conjectures. We find that the rate of complexification according to both of
these conjectures has UV divergences, whereas the instantaneous energy is UV
finite. This implies that neither the \textit{complexity equals action} nor
\textit{complexity equals volume} conjecture is consistent with the conjectured
bound on the rate of complexification. |
The two-loop six-point amplitude in ABJM theory: In this paper we present the first analytic computation of the six-point
two-loop amplitude of ABJM theory. We show that the two-loop amplitude consist
of corrections proportional to two distinct local Yangian invariants which can
be identified as the tree- and the one-loop amplitude respectively. The
two-loop correction proportional to the tree-amplitude is identical to the
one-loop BDS result of N=4 SYM plus an additional remainder function, while the
correction proportional to the one-loop amplitude is finite. Both the remainder
and the finite correction are dual conformal invariant, which implies that the
two-loop dual conformal anomaly equation for ABJM is again identical to that of
one-loop N=4 SYM, as was first observed at four-point. We discuss the theory on
the Higgs branch, showing that its amplitudes are infrared finite, but equal,
in the small mass limit, to those obtained in dimensional regularization. | Conformally Exact Results for SL(2,R)\times SO(1,1)^{d-2}/SO(1,1) Coset
Models: Using the conformal invariance of the $SL(2,R)\otimes SO(1,1)^{d-2}/SO(1,1)$
coset models we calculate the conformally exact metric and dilaton, to all
orders in the $1/k$ expansion. We consider both vector and axial gauging. We
find that these cosets represent two different space--time geometries: ($2d$
black hole)$\otimes \IR^{d-2}$ for the vector gauging and ($3d$ black
string)$\otimes \IR^{d-3}$ for the axial one. In particular for $d=3$ and for
the axial gauging one obtains the exact metric and dilaton of the charged black
string model introduced by Horne and Horowitz. If the value of $k$ is finite we
find two curvature singularities which degenerate to one in the semi--classical
$k\to \infty$ limit. We also calculate the reflection and transmission
coefficients for the scattering of a tachyon wave and using the Bogoliubov
transformation we find the Hawking temperature. |
A Conformal Field Theory of a Rotating Dyon: A conformal field theory representing a four-dimensional classical solution
of heterotic string theory is presented. The low-energy limit of this solution
has U(1) electric and magnetic charges, and also nontrivial axion and dilaton
fields. The low-energy metric contains mass, NUT and rotation parameters. We
demonstrate that this solution corresponds to part of an extremal limit of the
Kerr-Taub-NUT dyon solution. This limit displays interesting `remnant'
behaviour, in that asymptotically far away from the dyon the angular momentum
vanishes, but far down the infinite throat in the neighbourhood of the horizon
(described by our CFT) there is a non-zero angular velocity. A further natural
generalization of the CFT to include an additional parameter is presented, but
the full physical interpretation of its role in the resulting low energy
solution is unclear. | Wall-Crossing Invariants from Spectral Networks: A new construction of BPS monodromies for 4d ${\mathcal N}=2$ theories of
class S is introduced. A novel feature of this construction is its manifest
invariance under Kontsevich-Soibelman wall crossing, in the sense that no
information on the 4d BPS spectrum is employed. The BPS monodromy is encoded by
topological data of a finite graph, embedded into the UV curve $C$ of the
theory. The graph arises from a degenerate limit of spectral networks,
constructed at maximal intersections of walls of marginal stability in the
Coulomb branch of the gauge theory. The topology of the graph, together with a
notion of framing, encode equations that determine the monodromy. We develop an
algorithmic technique for solving the equations, and compute the monodromy in
several examples. The graph manifestly encodes the symmetries of the monodromy,
providing some support for conjectural relations to specializations of the
superconformal index. For $A_1$-type theories, the graphs encoding the
monodromy are "dessins d'enfants" on $C$, the corresponding Strebel
differentials coincide with the quadratic differentials that characterize the
Seiberg-Witten curve. |
Comment on "Dirac fermions in Som-Raychaudhuri space-time with scalar
and vector potential and the energy momentum distributions": We point out a misleading treatment and incorrect expressions in a recent
paper published in this Journal [Eur. Phys. J. C (2019) 79: 541] regarding
solutions for the Dirac equation in presence of scalar and vector potentials in
a class of flat G\"odel-type space-time called Som-Raychaudhuri space-time.
Following the appropriate procedure we obtain the solution for this system. | Supersymmetric Wilson loops in N=4 SYM and pure spinors: We study supersymmetric Wilson loop operators in four-dimensional N=4 super
Yang-Mills theory. We show that the contour of a supersymmetric Wilson loop is
either an orbit of some conformal transformation of the space-time (case I), or
an arbitrary contour in the subspace where local superalgebra generator is a
pure spinor (case II). In the more interesting case II we find and classify all
pairs (Q,W) of the supercharges and the corresponding operators modulo the
action of the global symmetry group. |
One-instanton test of the exact prepotential for N=2 SQCD coupled to a
symmetric tensor hypermultiplet: Using the ADHM instanton calculus, we evaluate the one-instanton contribution
to the low-energy effective prepotential of N=2 supersymmetric SU(N) Yang-Mills
theory with N_F flavors of hypermultiplets in the fundamental representation
and a hypermultiplet in the symmetric rank two tensor representation. For
N_F<N-2, when the theory is asymptotically free, our result is compared with
the exact solution that was obtained using M-theory and we find complete
agreement. | Anomaly Cancellation and gauge group of the standard model in NCG: It is well known that anomaly cancellation {\it almost} determines the
hypercharges in the standard model. A related (and somewhat more stronger)
phenomenon takes place in Connes' NCG framework: unimodularity (a technical
condition on elements of the algebra) is {\it strictly} equivalent to anomaly
cancellation (in the absence of right-handed neutrinos); and this in turn
reduces the symmetry group of the theory to the standard $SU(3)\times SU(2)
\times U(1)$. |
Quantum Field Theory on Noncommutative Space-Times and the Persistence
of Ultraviolet Divergences: We study properties of a scalar quantum field theory on two-dimensional
noncommutative space-times. Contrary to the common belief that noncommutativity
of space-time would be a key to remove the ultraviolet divergences, we show
that field theories on a noncommutative plane with the most natural
Heisenberg-like commutation relations among coordinates or even on a
noncommutative quantum plane with $E_q(2)$-symmetry have ultraviolet
divergences, while the theory on a noncommutative cylinder is ultraviolet
finite. Thus, ultraviolet behaviour of a field theory on noncommutative spaces
is sensitive to the topology of the space-time, namely to its compactness. We
present general arguments for the case of higher space-time dimensions and as
well discuss the symmetry transformations of physical states on noncommutative
space-times. | Coherent States Expectation Values as Semiclassical Trajectories: We study the time evolution of the expectation value of the anharmonic
oscillator coordinate in a coherent state as a toy model for understanding the
semiclassical solutions in quantum field theory. By using the deformation
quantization techniques, we show that the coherent state expectation value can
be expanded in powers of $\hbar$ such that the zeroth-order term is a classical
solution while the first-order correction is given as a phase-space Laplacian
acting on the classical solution. This is then compared to the effective action
solution for the one-dimensional $\f^4$ perturbative quantum field theory. We
find an agreement up to the order $\l\hbar$, where $\l$ is the coupling
constant, while at the order $\l^2 \hbar$ there is a disagreement. Hence the
coherent state expectation values define an alternative semiclassical dynamics
to that of the effective action. The coherent state semiclassical trajectories
are exactly computable and they can coincide with the effective action
trajectories in the case of two-dimensional integrable field theories. |
Recursion Relations from Space-time Supersymmetry: We describe a method for obtaining relations between higher derivative
interactions in supersymmetric effective actions. The method extends to all
orders in the momentum expansion. As an application, we consider the string
coupling dependence of the \hat{G}^{2k} \lambda^{16} interaction in type IIB
string theory. Using supersymmetry, we show that each of these interactions
satisfies a Poisson equation on the moduli space with sources determined by
lower momentum interactions. We argue that these protected couplings are only
renormalized by a finite number of string loops together with non-perturbative
terms. Finally, we explore some consequences of the Poisson equation for low
values of k. | The Einstein equations for generalized theories of gravity and the
thermodynamic relation $δQ = T δS$ are equivalent: We show that the equations of motion of generalized theories of gravity are
equivalent to the thermodynamic relation $\delta Q = T \delta S$. Our proof
relies on extending previous arguments by using a more general definition of
the Noether charge entropy. We have thus completed the implementation of
Jacobson's proposal to express Einstein's equations as a thermodynamic equation
of state. Additionally, we find that the Noether charge entropy obeys the
second law of thermodynamics if the matter energy momentum tensor obeys the
null energy condition. Our results support the idea that gravitation on a
macroscopic scale is a manifestation of the thermodynamics of the vacuum. |
Gravitational Anomalies, Hawking Radiation, and Spherically Symmetric
Black Holes: Motivated by the recent work of Robinson and Wilczek, we evaluate the
gravitational anomaly of a chiral scalar field in a Vaidya spacetime of
arbitrary mass function, and thus the outgoing flux from the time-dependent
horizon in that spacetime. We show that this flux differs from that of a
perfect blackbody at a fixed temperature. When this flux is taken into account,
general covariance in that spacetime is restored. We also generalize their
results to the most general static, and spherically symmetric spacetime. | Bulk and Brane Decay of a (4+n)-Dimensional Schwarzschild-De-Sitter
Black Hole: Scalar Radiation: In this paper, we extend the idea that the spectrum of Hawking radiation can
reveal valuable information on a number of parameters that characterize a
particular black hole background - such as the dimensionality of spacetime and
the value of coupling constants - to gain information on another important
aspect: the curvature of spacetime. We investigate the emission of Hawking
radiation from a D-dimensional Schwarzschild-de-Sitter black hole emitted in
the form of scalar fields, and employ both analytical and numerical techniques
to calculate greybody factors and differential energy emission rates on the
brane and in the bulk. The energy emission rate of the black hole is
significantly enhanced in the high-energy regime with the number of spacelike
dimensions. On the other hand, in the low-energy part of the spectrum, it is
the cosmological constant that leaves a clear footprint, through a
characteristic, constant emission rate of ultrasoft quanta determined by the
values of black hole and cosmological horizons. Our results are applicable to
"small" black holes arising in theories with an arbitrary number and size of
extra dimensions, as well as to pure 4-dimensional primordial black holes,
embedded in a de Sitter spacetime. |
Fusion rules for N=2 superconformal modules: In this note we calculate the fusion coefficients for minimal series
representations of the N=2 superconformal algebra by using a modified
Verlinde's formula, and obtain associative and commutative fusion algebras with
non-negative integral fusion coefficients at each level. Some references are
added. | Conformally Soft Theorem In Gravity: A central feature of scattering amplitudes in gravity or gauge theory is the
existence of a variety of energetically soft theorems which put constraints on
the amplitudes. Celestial amplitudes which are obtained from momentum-space
amplitudes by a Mellin transform over the external particle energies cannot
obey the usual energetically soft theorems. Instead, the symmetries of the
celestial sphere imply that the scattering of conformally soft particles whose
conformal weights under the 4D Lorentz group SL(2,C) are taken to zero obey
special relations. Such conformally soft theorems have recently been found for
gauge theory. Here, I show conformally soft factorization of celestial
amplitudes for gravity and identify it as the celestial analogue of Weinberg's
soft graviton theorem. |
Kaluza-Klein towers in warped spaces with metric singularities: The version of the warp model that we proposed to explain the mass scale
hierarchy has been extended by the introduction of one or more singularities in
the metric. We restricted ourselves to a real massless scalar field supposed to
propagate in a five dimensional bulk with the extradimension being compactified
on a strip or on a circle. With the same emphasis on the hermiticity and
commutativity properties of the Kakuza Klein operators, we have established all
the allowed boundary conditions to be imposed on the fields. From them, for
given positions of the singularities, one can deduce either mass eigenvalues
building up a Kaluza Klein tower, or a tachyon, or a zero mass state. Assuming
the Planck mass to be the high mass scale and by a choice, unique for all
boundary conditions, of the major warp parameters, the low lying mass
eigenvalues are of the order of the TeV, in this way explaining the mass scale
hierarchy. In our model, the physical masses are related to the Kaluza Klein
eigenvalues, depending on the location of the physical brane which is an
arbitrary parameter of the model. Illustrative numerical calculations are given
to visualize the structure of Kaluza Klein mass eigenvalue towers. Observation
at high energy colliders like LHC of a mass tower with its characteristic
structure would be the fingerprint of the model. | Planar field theories with space-dependent noncommutativity: We study planar noncommutative theories such that the spatial coordinates
${\hat x}_1$, ${\hat x}_2$ verify a commutation relation of the form: $[{\hat
x}_1, {\hat x}_2] = i \theta ({\hat x}_1,{\hat x}_2)$. Starting from the
operatorial representation for dynamical variables in the algebra generated by
${\hat x}_1$ and ${\hat x}_2$, we introduce a noncommutative product of
functions corresponding to a specific operator-ordering prescription. We define
derivatives and traces, and use them to construct scalar-field actions. The
resulting expressions allow one to consider situations where an expansion in
powers of $\theta$ and its derivatives is not necessarily valid. In particular,
we study in detail the case when $\theta$ vanishes along a linear region. We
show that, in that case, a scalar field action generates a boundary term,
localized around the line where $\theta$ vanishes. |
Standard Model Fermions and N=8 supergravity: In a scheme originally proposed by M. Gell-Mann, and subsequently shown to be
realized at the SU(3)xU(1) stationary point of maximal gauged SO(8)
supergravity by N. Warner and one of the present authors, the 48 spin 1/2
fermions of the theory remaining after the removal of eight Goldstinos can be
identified with the 48 quarks and leptons (including right-chiral neutrinos) of
the Standard Model, provided one identifies the residual SU(3) with the
diagonal subgroup of the color group SU(3)_c and a family symmetry SU(3)_f.
However, there remained a systematic mismatch in the electric charges by a
spurion charge of $\pm$1/6. We here identify the `missing' U(1) that rectifies
this mismatch, and that takes a surprisingly simple, though unexpected form. | On the Scalar Spectrum of the Y^{p,q} Manifolds: The spectra of supergravity modes in anti de Sitter (AdS) space on a
five-sphere endowed with the round metric (which is the simplest 5d
Sasaki-Einstein space) has been studied in detail in the past. However for the
more general class of cohomogeneity one Sasaki-Einstein metrics on S^2 x S^3,
given by the Y^{p, q} class, a complete study of the spectra has not been
attempted. Earlier studies on scalar spectrum were restricted to only the first
few eigenstates. In this paper we take a step in this direction by analysing
the full scalar spectrum on these spaces. However it turns out that finding the
exact solution of the corresponding eigenvalue problem in closed form is not
feasible since the computation of the eigenvalues of the Laplacian boils down
to the analysis of a one-dimensional operator of Heun type, whose spectrum
cannot be computed in closed form. However, despite this analytical obstacle,
we manage to get both lower and upper bounds on the eigenvalues of the scalar
spectrum by comparing the eigenvalue problem with a simpler, solvable system.
We also briefly touch upon various other new avenues such as non-commutative
and dipole deformations as well as possible non-conformal extensions of these
models. |
Complete factorization of equations of motion in Wess-Zumino theory: We prove that the equations of motion describing domain walls in a
Wess-Zumino theory involving only one chiral matter multiplet can be factorized
into first order Bogomol'nyi equations, so that all the topological defects are
of the Bogomol'nyi-Prasad-Sommerfield type. | Dynamical Realizability for Quantum Measurement and Factorization of
Evolution Operator: By building a general dynamical model for quantum measurement process,it is
shown that the factorization of reduced evolution operator sufficiently results
in the quantum mechanical realization of the wave packet collapse and the state
correlation between the measured system and the measuring
instrument-detector.This realizability is largely independent of the details of
both the interaction and Hamiltonian of detector. The Coleman-Hepp model and
all its generalizations are only the special cases of the more universal model
given in this letter.An explicit example of this model is finally given in
connection with coherent state. |
Klein-Gordon particles in mixed vector-scalar inversely linear
potentials: The problem of a spinless particle subject to a general mixing of vector and
scalar inversely linear potentials in a two-dimensional world is analyzed.
Exact bounded solutions are found in closed form by imposing boundary
conditions on the eigenfunctions which ensure that the effective Hamiltonian is
Hermitian for all the points of the space. The nonrelativistic limit of our
results adds a new support to the conclusion that even-parity solutions to the
nonrelativistic one-dimensional hydrogen atom do not exist. | Order-chaos transitions in field theories with topological terms: a
dynamical systems approach: We present a comparative study of the dynamical behaviour of topological
systems of recent interest, namely the non-Abelian Chern-Simons Higgs system
and the Yang-Mills Chern-Simons Higgs system. By reducing the full field
theories to temporal differential systems using the assumption of spatially
homogeneous fields , we study the Lyapunov exponents for two types of initial
conditions. We also examine in minute detail the behaviour of the Lyapunov
spectra as a function of the various coupling parameters in the system. We
compare and contrast our results with those for Abelian Higgs, Yang-Mills Higgs
and Yang-Mills Chern-Simons systems which have been discussed by other authors
recently. The role of the various terms in the Hamiltonians for such systems in
determining the order-disorder transitions is emphasized and shown to be
counter-intuitive in the Yang-Mills Chern-Simons Higgs systems. |
Properties of Asymptotically Flat Two-Dimensional Black Holes: We investigate properties of two-dimensional asymptotically flat black holes
which arise in both string theory and in scale invariant theories of gravity.
By introducing matter sources in the field equations we show how such objects
can arise as the endpoint of gravitational collapse. We examine the motion of
test particles outside the horizons, and show that they fall through in a
finite amount of proper time and an infinite amount of coordinate time. We also
investigate the thermodynamic and quantum properties, which give rise to a
fundamental length scale. The 't Hooft prescription for cutting off eigenmodes
of particle wave functions is shown to be source dependent, unlike the
four-dimensional case. The relationship between these black holes and those
considered previously in $(1+1)$ dimensions is discussed. | On the Renormalization of a Bosonized Version of the Chiral
Fermion-Meson Model at Finite Temperature: Feynman's functional formulation of statistical mechanics is used to study
the renormalizability of the well known Linear Chiral Sigma Model in the
presence of fermionic fields at finite temperature in an alternative way. It is
shown that the renormalization conditions coincide with those of the zero
temperature model. |
Resolution of the strong CP and U(1) problems: Definition of the determinant of Euclidean Dirac operator in the nontrivial
sector of gauge fields suffers from an inherent ambiguity. The popular
Osterwalder-Schrader (OS) recipe for the conjugate Dirac field leads to the
option of a vanishing determinant. We propose a novel representation for the
conjugate field which depends linearly on the Dirac field and yields a
nonvanishing determinant in the nontrivial sector. Physics, it appears, chooses
this second option becuase the novel representation leads to a satisfactory
resolution of two outstanding problems, the strong CP and U(1) problems,
attributed to instanton effects. | From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited: Recently, loop integrands for certain Yang-Mills scattering amplitudes and
correlation functions have been shown to be systematically expressible in dlog
form, raising the possibility that these loop integrals can be performed
directly without Feynman parameters. We do so here to give a new description of
the planar 1-loop MHV amplitude in N = 4 super Yang-Mills theory. We explicitly
incorporate the standard Feynman i epsilon prescription into the integrands. We
find that the generic MHV diagram contributing to the 1-loop MHV amplitude,
known as Kermit, is dual conformal invariant up to the choice of reference
twistor explicit in our axial gauge (the generic MHV diagram was already known
to be finite). The new formulae for the amplitude are nontrivially related to
previous ones in the literature. The divergent diagrams are evaluated using
mass regularization. Our techniques extend directly to higher loop diagrams,
and we illustrate this by sketching the evaluation of a non-trivial 2-loop
example. We expect this to lead to a simple and efficient method for computing
amplitudes and correlation functions with less supersymmetry and without the
assumption of planarity. |
Graviton Trispectrum from Gluons: The tree-level wavefunction coefficient for four gravitons in de Sitter space
was recently bootstrapped using the Cosmological Optical Theorem, flat space
limit, and Manifestly Local Test \cite{Bonifacio:2022vwa}. Inspired by the
double copy for scattering amplitudes, we derive a compact new expression for
this quantity starting from the wavefunction coefficient for gluons. | Gauge Symmmetry and Supersymmetry Breaking by Discrete Symmetry: We study the principles of the gauge symmetry and supersymmetry breaking due
to the local or global discrete symmetries on the extra space manifold. We show
that the gauge symmetry breaking by Wilson line is the special case of the
discrete symmetry approach where all the discrete symmetries are global and act
freely on the extra space manifold. As applications, we discuss the N=2
supersymmetric SO(10) and $E_8$ breaking on the space-time $M^4\times A^2$ and
$M^4\times D^2$, and point out that similarly one can study any N=2
supersymmetric $SO(M)$ breaking. We also comment on the one-loop effective
potential, the possible questions and generalization. |
Redundant operators in the exact renormalisation group and in the f(R)
approximation to asymptotic safety: In this paper we review the definition and properties of redundant operators
in the exact renormalisation group. We explain why it is important to require
them to be eigenoperators and why generically they appear only as a consequence
of symmetries of the particular choice of renormalisation group equations. This
clarifies when Newton's constant and or the cosmological constant can be
considered inessential. We then apply these ideas to the Local Potential
Approximation and approximations of a similar spirit such as the f(R)
approximation in the asymptotic safety programme in quantum gravity. We show
that these approximations can break down if the fixed point does not support a
`vacuum' solution in the appropriate domain: all eigenoperators become
redundant and the physical space of perturbations collapses to a point. We show
that this is the case for the recently discovered lines of fixed points in the
f(R) flow equations. | N=4 Supersymmetric Yang-Mills Multiplet in Non-Adjoint Representations: We formulate a theory for N=4 supersymmetric Yang-Mills multiplet in a
non-adjoint representation R of SO(N) as an important application of our
recently-proposed model for N=1 supersymmetry. This system is obtained by
dimensional reduction from an N=1 supersymmetric Yang-Mills multiplet in
non-adjoint representation in ten dimensions. The consistency with
supersymmetry requires that the non-adjoint representation R with the indices
i, j, ... satisfy the three conditions \eta^{i j} = \delta^{i j}, (T^I)^{i j} =
- (T^I)^{j i} and (T^I)^{[ i j |} (T^I)^{| k ] l} = 0 for the metric \eta^{i j}
and the generators T^I, which are the same as the N=1 case. |
Quantization of the Closed Mini-Superspace Models as Bound States: Wheeler-DeWitt equation is applied to $k > 0$ Friedmann Robertson Walker
metric with various types of matter. It is shown that if the Universe ends in
the matter dominated era (e.g., radiation or pressureless gas) with zero
cosmological constant, then the resulting Wheeler-DeWitt equation describes a
bound state problem. As solutions of a non-degenerate bound state system, the
eigen-wave functions are real (Hartle-Hawking) and the usual issue associated
with the ambiguity in the boundary conditions for the wave functions is
resolved. Furthermore, as a bound state problem, there exists a quantization
condition that relates the curvature of the three space with the energy density
of the Universe. Incorporating a cosmological constant in the early Universe
(inflation) is given as a natural explanation for the large quantum number
associated with our Universe, which resulted from the quantization condition.
It is also shown that if there is a cosmological constant $\Lambda > 0$ in
our Universe that persists for all time, then the resulting Wheeler-DeWitt
equation describes a non-bound state system, regardless of the magnitude of the
cosmological constant. As a consequence, the wave functions are in general
complex (Vilenkin) and the initial conditions for wave functions are a free
parameters not determined by the formalism. | The noncovariant gauges in 3-form theories: We study the 3-form gauge theory in the context of generalized BRST
formulation. We construct the finite field-dependent BRST (FFBRST) symmetry for
such a theory. The generating functional for 3-form gauge theory in
noncovariant gauge is obtained from that of in covariant gauge. We further
extend the results by considering 3-form gauge theory in the context of
Batalin-Vilkovisky (BV) formulation. |
Phase Information in Cosmological Collider Signals: Massive particles produced during the cosmic inflation can imprint in the
primordial non-Gaussianities as characteristic oscillating functions of various
momentum ratios, known as cosmological collider signals. We initiate a study of
the phase of the oscillating signals which can be unambiguously defined and
measured. The phase can provide useful new information about the spin and the
couplings of the intermediate heavy particles that cannot be obtained from the
signal frequency and angular dependences alone. We also present new analytical
results for full nonlocal signals from two typical 1-loop processes, enabling
precise determination of the signal phase away from the squeezed limit. | The Proper Time Equation and the Zamolodchikov Metric: The connection between the proper time equation and the Zamolodchikov metric
is discussed. The connection is two-fold: First, as already known, the proper
time equation is the product of the Zamolodchikov metric and the
renormalization group beta function. Second, the condition that the two-point
function is the Zamolodchikov metric, implies the proper time equation. We
study the massless vector of the open string in detail. In the exactly
calculable case of a uniform electromgnetic field strength we recover the
Born-Infeld equation. We describe the systematics of the perturbative
evaluation of the gauge invariant proper time equation for the massless vector
field. The method is valid for non-uniform fields and gives results that are
exact to all orders in derivatives. As a non trivial check, we show that in the
limit of uniform fields it reproduces the lowest order Born-Infeld equation. |
Nonpropagation of scalar in the deformed Hořava-Lifshitz gravity: We study the propagation of a scalar, the trace of $h_{ij}$ in the deformed
Ho\v{r}ava-Lifshitz gravity with coupling constant $\lambda$. It turns out that
this scalar is not a propagating mode in the Minkowski spacetime background. In
this work, we do not choose a gauge-fixing to identify the physical degrees of
freedom and instead, make it possible by substituting the constraints into the
quadratic Lagrangian. | Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various
Dimensions IV - Topological Black Holes with and without Cosmological Term: We study black hole solutions in the Einstein gravity with Gauss-Bonnet term,
the dilaton and a positive "cosmological constant" in various dimensions.
Physically meaningful black holes with a positive cosmological term are
obtained only for those in static spacetime with $(D-2)$-dimensional hyperbolic
space of negative curvature and $D>4$. We construct such black hole solutions
of various masses numerically in $D=5,6$ and 10 dimensional spacetime and
discuss their properties. In spite of the positive cosmological constant the
spacetime approach anti-de Sitter spacetime asymptotically. The black hole
solutions exist for a certain range of the horizon radius, i.e., there are
lower and upper bounds for the size of black holes. We also argue that it is
quite plausible that there is no black hole solution for hyperbolic space in
the case of no cosmological constant. |
Fermionic greybody factors in Schwarzschild acoustic black holes: In Schwarzschild's acoustic black hole (SABH) spacetime, we investigate the
wave dynamics for the fermions. To this end, we first take into account the
Dirac equation in the SABH by employing a null tetrad in the Newman-Penrose
(NP) formalism. Then, we consider the Dirac and Rarita Schwinger equations,
respectively. The field equations are reduced to sets of radial and angular
equations. By using the analytical solution of the angular equation set, we
decouple the radial wave equations and obtain the one-dimensional
Schr\"{o}dinger like wave equations with their effective potentials. The
obtained effective potentials are graphically depicted and analyzed. Finally,
we investigate the fermionic greybody factors (GFs) radiated by the SABH
spacetime. A thorough investigation is conducted into how the acoustic tuning
parameter affects the GFs of the SABH spacetime. Both the semi-analytic WKB
method and bounds for the GFs are used to produce the results, which are shown
graphically and discussed. | Limits to the observation of the Unruh radiation via first-quantized
hydrogen-like atoms: We consider ionized hydrogen-like atoms accelerated by an external electric
field to detect Unruh radiation. By applying quantum field theory in the
Rindler spacetime, we show that the first-quantized description for
hydrogen-like atoms cannot always be adopted. This is due to the
frame-dependent definition of particles as positive and negative frequency
field modes. We show how to suppress such a frame-dependent effect by
constraining the atomic ionization and the electric field. We identify the
physical regimes with nonvanishing atomic excitation probability due to the
Unruh electromagnetic background. We recognize the observational limits for the
Unruh effect via first-quantized atomic detectors, which appear to be
compatible with current technology. Notably, the non-relativistic energy
spectrum of the atom cannot induce coupling with the thermal radiation, even
when special relativistic and general relativistic corrections are considered.
On the contrary, the coupling with the Unruh radiation arises because of
relativistic hyperfine splitting. |
Anharmonic Oscillators, Spectral Determinant and Short Exact Sequence of
affine U_q(sl_2): We prove one of conjectures, raised by Dorey and Tateo in the connection
among the spectral determinant of anharmonic oscillator and vacuum eigenvalues
of transfer matrices in field theory and statistical mechanics. The exact
sequence of $U_q(\hat{sl}_2)$ plays a fundamental role in the proof. | Fusion Rules for Affine sl(2|1;C) at Fractional Level k=-1/2: We calculate fusion rules for the admissible representations of the affine
superalgebra sl(2|1;C) at fractional level k=-1/2 in the Ramond sector. By
representing 3-point correlation functions involving a singular vector as the
action of differential operators on the sl(2|1;C) invariant 3-point function,
we obtain conditions on permitted quantum numbers involved. We find that in
this case the primary fields close under fusion. |
A Heterotic N=2 String with Space-Time Supersymmetry: We reconsider the issue of embedding space-time fermions into the
four-dimensional N=2 world-sheet supersymmetric string. A new heterotic theory
is constructed, taking the right-movers from the N=4 topological extension of
the conventional N=2 string but a c=0 conformal field theory supporting
target-space supersymmetry for the left-moving sector. The global bosonic
symmetry of the full formalism proves to be U(1,1), just as in the usual N=2
string. Quantization reveals a spectrum of only two physical states, one boson
and one fermion, which fall in a multiplet of (1,0) supersymmetry. | Probing Gravitational Interactions of Elementary Particles: The gravitational interactions of elementary particles are suppressed by the
Planck scale M_P ~ 10^18 GeV and are typically expected to be far too weak to
be probed by experiments. We show that, contrary to conventional wisdom, such
interactions may be studied by particle physics experiments in the next few
years. As an example, we consider conventional supergravity with a stable
gravitino as the lightest supersymmetric particle. The next-lightest
supersymmetric particle (NLSP) decays to the gravitino through gravitational
interactions after about a year. This lifetime can be measured by stopping
NLSPs at colliders and observing their decays. Such studies will yield a
measurement of Newton's gravitational constant on unprecedentedly small scales,
shed light on dark matter, and provide a window on the early universe. |
Finite volume partition functions and Itzykson-Zuber integrals: We find the finite volume QCD partition function for arbitrary quark masses.
This is a generalization of a result obtained by Leutwyler and Smilga for equal
quark masses. Our result is derived in the sector of zero topological charge
using a generalization of the Itzykson-Zuber integral appropriate for arbitrary
complex matrices. We present a conjecture regarding the result for arbitrary
topological charge which reproduces the Leutwyler-Smilga result in the limit of
equal quark masses. We derive a formula of the Itzykson-Zuber type for
arbitrary {\em rectangular} complex matrices, extending the result of Guhr and
Wettig obtained for {\em square} matrices. | $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS$_3$ gravity: We study the $T\bar{T}$ deformation of the chiral bosons and show the
equivalence between the chiral bosons of opposite chiralities and the scalar
fields at the Hamiltonian level under the deformation. We also derive the
deformed Lagrangian of more generic theories which contain an arbitrary number
of chiral bosons to all orders. By using these results, we derive the
$T\bar{T}$ deformed boundary action of the AdS$_3$ gravity theory in the
Chern-Simons formulation. We compute the deformed one-loop torus partition
function, which satisfies the $T\bar{T}$ flow equation up to the one-loop
order. Finally, we calculate the deformed stress tensor of a solution
describing a BTZ black hole in the boundary theory, which coincides with the
boundary stress tensor derived from the BTZ black hole with a finite cutoff. |
Exact $β$-functions for ${\cal N}=1$ supersymmetric theories finite
in the lowest loops: We consider a one-loop finite ${\cal N}=1$ supersymmetric theory in such a
renormalization scheme that the first $L$ contributions to the gauge
$\beta$-function and the first $(L-1)$ contributions to the anomalous dimension
of the matter superfields and to the Yukawa $\beta$-function vanish. It is
demonstrated that in this case the NSVZ equation and the exact equation for the
Yukawa $\beta$-function in the first nontrivial order are valid for an
arbitrary renormalization prescription respecting the above assumption. This
implies that under this assumption the $(L+1)$-loop contribution to the gauge
$\beta$-function and the $L$-loop contribution to the Yukawa $\beta$-function
are always expressed in terms of the $L$-loop contribution to the anomalous
dimension of the matter superfields. This statement generalizes the result of
Grisaru, Milewski, and Zanon that for a theory finite in $L$ loops the
$(L+1)$-loop contribution to the $\beta$-function also vanishes. In particular,
it gives a simple explanation why their result is valid although the NSVZ
equation does not hold in an arbitrary subtraction scheme. | New Rotating Non-Extremal Black Holes in D=5 Maximal Gauged Supergravity: We obtain new non-extremal rotating black hole solutions in maximal
five-dimensional gauged supergravity. They are characterised by five
parameters, associated with the mass, the two angular momenta, and two
independently-specifiable charge parameters. Two of the three charges
associated with the U(1)^3 Cartan subgroup of the SO(6) gauge group are equal,
whilst the third can be independently specified. These new solutions generalise
all the previously-known rotating solutions in five-dimensional gauged
supergravity with independent angular momenta. They describe regular black
holes, provided the parameters lie in appropriate ranges so that naked
singularities and closed-timelike curves (CTCs) are avoided. We also construct
the BPS limit, and show that regular supersymmetric black holes or topological
solitons arise if the parameters are further restricted in an appropriate
manner. |
Integrable aspects of the scaling q-state Potts models II: finite-size
effects: We continue our discussion of the q-state Potts models for q <= 4, in the
scaling regimes close to their critical and tricritical points. In a previous
paper, the spectrum and full S-matrix of the models on an infinite line were
elucidated; here, we consider finite-size behaviour. TBA equations are proposed
for all cases related to phi(21) and phi(12) perturbations of unitary minimal
models. These are subjected to a variety of checks in the ultraviolet and
infrared limits, and compared with results from a recently-proposed nonlinear
integral equation. A nonlinear integral equation is also used to study the
flows from tricritical to critical models, over the full range of q. Our
results should also be of relevance to the study of the off-critical dilute A
models in regimes 1 and 2. | Abelian Higgs Model Effective Potential in the Presence of Vortices: We determine the contribution of nontrivial vacuum (topological) excitations,
more specifically vortex--strings of the Abelian Higgs model in 3+1 dimensions,
to the functional partition function. By expressing the original action in
terms of dual transformed fields we make explicit in the equivalent action the
contribution of the vortex--strings excitations of the model. The effective
potential of an appropriately defined local vacuum expectation value of the
vortex--string field in the dual transformed action is then evaluated both at
zero and finite temperatures and its properties discussed in the context of the
finite temperature phase transition. |
Three functions in dilaton gravity: The good, the bad and the muggy: Dilaton gravity in two dimensions is briefly reviewed from the perspective of
three dilaton potentials: One determines classical physics ("the good", denoted
by w), the second is relevant for semi-classical (and quantum) effects ("the
muggy", denoted by I) and the third could be responsible for nonperturbative
quantum effects ("the bad", denoted by Z).
This paper is based upon lectures given in Cernowitz in October/November 2002
at The XIV International Hutsulian Workshop Mathematical Theories and their
Physical and Technical Applications. | Folded Strings: Recent progress on the complete set of solutions of two dimensional classical
string theory in any curved spacetime is reviewed. When the curvature is smooth
the string solutions are deformed folded string solutions as compared to flat
spacetime folded strings that were known for 19 years. However, surprizing new
stringy behavior becomes evident at singularities such as black holes. The
global properties of these solutions require that the ``bare singularity
region"of the black hole be included along with the usual black hole spacetime.
The mathematical structure needed to describe the solutions include a recursion
relation that is analogous to the transfer matrix of lattice theories. This
encodes lattice properties on the worldsheet on the one hand and the geometry
of spacetime on the other hand. A case is made for the presence of folded
strings in the quantum theory of non-critical strings for $d\geq 2$. |
Anomaly Enforced Gaplessness for Background Flux Anomalies and Symmetry
Fractionalization: Anomalous symmetries are known to strongly constrain the possible IR behavior
along any renormalization group (RG) flow. Recently, the extension of the
notion of symmetry in QFT has provided new types of anomalies with a
corresponding new class of constraints on RG flows. In this paper, we derive
the constraints imposed on RG flows from anomalies that can only be activated
in the presence of specific background fluxes even though they do not
necessarily correspond to a symmetry. We show that such anomalies can only be
matched by gapped theories that exhibit either spontaneous symmetry breaking or
symmetry fractionalization. In addition, we exhibit previously unstudied
examples of these flux background anomalies that arise in $4d$ QCD and $4d$
SUSY QCD. | Hyperscaling violating Lifshitz holography: We present an overview of the construction of the general holographic
dictionary for asymptotically locally Lifshitz and hyperscaling violating
Lifshitz backgrounds with arbitrary dynamical exponents $z$ and $\theta$,
compatible with the null energy condition, which was recently developed in
[1,2]. A concrete definition of asymptotically locally Lifshitz and
hyperscaling violating Lifshitz backgrounds is provided in the context of a
generic bottom-up Einstein-Proca-Dilaton theory, and a systematic procedure for
solving the radial Hamilton-Jacobi equation via a covariant expansion in
eigenfunctions of two commuting operators is presented. The resulting
asymptotic solution of the Hamilton-Jacobi equation is subsequently used to
derive the full holographic dictionary, including the Fefferman-Graham
asymptotic expansions and the non-relativistic holographic Ward identities. |
Soliton Dynamics in a 2D Lattice Model with Nonlinear Interactions: This paper is concerned with a lattice model which is suited to
square-rectangle transformations characterized by two strain components. The
microscopic model involves nonlinear and competing interactions, which play a
key role in the stability of soliton solutions and emerge from interactions as
a function of particle pairs and noncentral type or bending forces. Special
attention is devoted to the continuum approximation of the two-dimensional
discrete system with the view of including the leading discreteness effects at
the continuum description. The long time evolution of the localized structures
is governed by an asymptotic integrable equation of the Kadomtsev-Petviashvili
I type which allows the explicit construction of moving multi-solitons on the
lattice. Numerical simulation performed at the discrete system investigate the
stability and dynamics of multi-soliton in the lattice space. | Baryon Binding Energy in Sakai-Sugimoto Model: The binding energy of baryon has been studied in the dual $AdS_5\times S^5$
string theory with a black hole interior. In this picture baryon is constructed
of a $D_5$ brane vertex wrapping on $S^5$ and $N_c$ fundamental strings
connected to it. Here, we calculate the baryon binding energy in Sakai-Sugimoto
model with a $D_4/D_8/\bar{D_8}$ in which the supersymmetry is completely
broken. Also we check the $T$ dependence of the baryon binding energy. We
believe that this model represents an accurate description of baryons due to
the existence of Chern-Simones coupling with the gauge field on the brane. We
obtain an analytical expression for the baryon binding energy . In that case we
plot the baryon binding energy in terms of radial coordinate. Then by using the
binding energy diagram, we determine the stability range for baryon
configuration. And also the position and energy of the stable equilibrium point
is obtained by the corresponding diagram. Also we plot the baryon binding
energy in terms of temperature and estimate a critical temperature in which the
baryon would be dissociated. |
Thermal ensemble of string gas in a magnetic field: We study the thermal ensemble of a gas of free strings in presence of a
magnetic field. We find that the thermodynamical partition function diverges
when the magnetic field exceeds some critical value $B_{\rm cr}$, which depends
on the temperature. We argue that there is a first-order phase transition with
a large latent heat. At the critical value an infinite number of states -all
states in a Regge trajectory- seem to become massless, which may be an
indication of recuperation of spontaneously broken symmetries. | Expanding plasmas from Anti de Sitter black holes: We introduce a new foliation of AdS$_5$ black holes such that the conformal
boundary takes the form of a $4$-dimensional FLRW spacetime with scale factor
$a(t)$. The foliation employs Eddington-Finkelstein-like coordinates and is
applicable to a large class of AdS black holes, supported by matter fields or
not, considerably extending previous efforts in the literature. We argue that
the holographic dual picture of a CFT plasma on a FLRW background provides an
interesting prototype to study the nonequilibrium dynamics of expanding plasmas
and use holographic renormalization to extract the renormalized energy-momentum
tensor of the dual plasma. We illustrate the procedure for three black holes of
interest, namely AdS-Schwarzschild, AdS-Gauss-Bonnet, and
AdS-Reissner-Nordstr\"om. For the latter, as a by-product, we show that the
nonequilibrium dynamics of a CFT plasma subject to a quench in the chemical
potential (i.e., a time-dependent chemical potential) resembles a cosmological
evolution with the scale factor $a(t)$ being inversely related to the quench
profile. |
Iterative structure of finite loop integrals: In this paper we develop further and refine the method of differential
equations for computing Feynman integrals. In particular, we show that an
additional iterative structure emerges for finite loop integrals. As a concrete
non-trivial example we study planar master integrals of light-by-light
scattering to three loops, and derive analytic results for all values of the
Mandelstam variables $s$ and $t$ and the mass $m$. We start with a recent
proposal for defining a basis of loop integrals having uniform transcendental
weight properties and use this approach to compute all planar two-loop master
integrals in dimensional regularization. We then show how this approach can be
further simplified when computing finite loop integrals. This allows us to
discuss precisely the subset of integrals that are relevant to the problem. We
find that this leads to a block triangular structure of the differential
equations, where the blocks correspond to integrals of different weight. We
explain how this block triangular form is found in an algorithmic way. Another
advantage of working in four dimensions is that integrals of different loop
orders are interconnected and can be seamlessly discussed within the same
formalism. We use this method to compute all finite master integrals needed up
to three loops. Finally, we remark that all integrals have simple Mandelstam
representations. | Quantum Mass corrections for C_2^(1) Affine Toda theory solitons: We calculate the quantum mass corrections to the solitons in the C_2^(1)
Affine Toda field theory. We find that the ratio of the masses of the two
solitons is not constant. |
The WKB approximation and tunneling in theories with non-canonical
kinetic terms: Tunneling is a fascinating aspect of quantum mechanics that renders the local
minima of a potential meta-stable, with important consequences for particle
physics, for the early hot stage of the universe, and more speculatively, for
the behavior of the putative multiverse. While this phenomenon has been studied
extensively for systems which have canonical kinetic terms, many theories of
fundamental physics contain fields with non-canonical kinetic structures. It is
therefore desirable to have a detailed framework for calculating tunneling
rates and initial states after tunneling for these theories. In this work, we
present such a rigorous formulation and illustrate its use by applying it to a
number of examples. | The local Callan-Symanzik equation: structure and applications: The local Callan-Symanzik equation describes the response of a quantum field
theory to local scale transformations in the presence of background sources.
The consistency conditions associated with this anomalous equation imply
non-trivial relations among the $\beta$-function, the anomalous dimensions of
composite operators and the short distance singularities of correlators. In
this paper we discuss various aspects of the local Callan-Symanzik equation and
present new results regarding the structure of its anomaly. We then use the
equation to systematically write the n-point correlators involving the trace of
the energy-momentum tensor. We use the latter result to give a fully detailed
proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also
correspond to CFTs. We also clarify the relation between the matrix entering
the gradient flow formula for the $\beta$-function and a manifestly positive
metric in coupling space associated with matrix elements of the trace of the
energy momentum tensor. |
Initial state propagators: It is possible to define a general initial state for a quantum field by
introducing a contribution to the action defined at an initial-time boundary.
The propagator for this theory is composed of two parts, one associated with
the free propagation of fields and another produced by the operators of this
initial action. The derivation of this propagator is shown for the case of a
translationally and rotationally invariant initial state. In addition to being
able to treat more general states, these techniques can also be applied to
effective field theories that start from an initial time. The eigenstates of a
theory with interacting heavy and light fields are different from the
eigenstates of the theory in the limit where the interactions vanish.
Therefore, a product of states of the noninteracting heavy and light theories
will usually contain excitations of the heavier state once the interactions are
included. Such excitations appear as nonlocal effects in the effective theory,
which are suppressed by powers of the mass of the heavy field. By appropriately
choosing the initial action, these excitations can be excised from the state
leaving just effects that would be produced by a local action of the lighter
fields. | On the full quantum trispectrum in multi-field DBI inflation: We compute the leading order connected four-point function of the primordial
curvature perturbation coming from the four-point function of the fields in
multi-field DBI inflation models. We confirm that the consistency relations in
the squeezed limit and in the counter-collinear limit hold as in single field
models thanks to special properties of the DBI action. We also study the
momentum dependence of the trispectra coming from the adiabatic, mixed and
purely entropic contributions separately and we find that they have different
momentum dependence. This means that if the amount of the transfer from the
entropy perturbations to the curvature perturbation is significantly large, the
trispectrum can distinguish multi-field DBI inflation models from single field
DBI inflation models. A large amount of transfer $T_{\mathcal{RS}} \gg 1 $
suppresses the tensor to scalar ratio $r \propto T_{\mathcal{RS}}^{-2}$ and the
amplitude of the bispectrum $f_{NL}^{equi} \propto T_{\mathcal{RS}}^{-2}$ and
so it can ease the severe observational constraints on the DBI inflation model
based on string theory. On the other hand, it enhances the amplitude of the
trispectrum $\tau_{NL}^{equi} \propto T_{\mathcal{RS}}^2 f_{NL}^{equi 2}$ for a
given amplitude of the bispectrum. |
Radiation of inertial scalar particles in the de Sitter universe: We investigate the radiation from an inertial scalar particle evolving in a
de Sitter expanding Universe. In the context of scalar QED the process is
generated by the first order term in the perturbation theory expansion of the
S-matrix. The partial transition probability is obtained and analysed, and
soft-photon emission is found to dominate overall. It has been argued that an
inertial particle evolving in dS spacetime loses physical momentum just as a
decelerated particle in Minkowski space does. It is thus expected that an
inertial charge will radiate in a similar way. We investigate the radiated
energy and make a qualitative comparison of the angular distribution of the
energy with the radiation pattern in the latter case. | Finite Temperature and Density Effects in Planar Q.E.D: The behavior of finite temperature planar electrodynamics is investigated. We
calculate the static as well as dynamic characteristic functions using real
time formalism. The temperature and density dependence of dielectric and
permeability functions, plasmon frequencies and their relation to the screening
length is determined. The radiative correction to the fermion mass is also
calculated. We also calculate the temperature dependence of the electron
(anyon) magnetic moment. Our results for the gyromagnetic ratio go smoothly to
the known result at zero temperature, $g=2$, in accordance with the general
expectation. |
Spectral Action and Gravitational effects at the Planck scale: We discuss the possibility to extend the spectral action up to energy close
to the Planck scale, taking also into account the gravitational effects given
by graviton exchange. Including this contribution in the theory, the coupling
constant unification is not compromised, but is shifted to the Planck scale
rendering all gauge couplings asymptotically free. In the scheme of
noncommutative geometry, the gravitational effects change the main standard
model coupling constants, leading to a restriction of the free parameters of
the theory compatible with the Higgs and top mass prediction. We also discuss
consequences for the neutrino mass and the see-saw mechanism. | Examples of 4D, N = 2 Holoraumy: We provide an introduction to the concepts of holoraumy tensors, Lorentz
covariant four-dimensional "Gadgets", and Gadget angles within the context of
4D N = 2 supermultiplets. This is followed by the calculation of the holoraumy
tensors, Gadgets, and Gadget angles for minimal off-shell supermultiplets. Four
tetrahedrons in four 3D subspaces of the Holoraumy lattice space are found. |
Dimensional regularization, Wilsonian RG, and the Naturalness/Hierarchy
problem: While it is usually stated that dimensional regularization (DR) has no direct
physical interpretation, consensus has recently grown on the idea that it might
be endowed with special physical properties that would provide the mechanism
that solves the naturalness/hierarchy problem. Comparing direct Wilsonian
calculations with the corresponding DR ones, we find that DR indeed has a
well-defined physical meaning, and we point out its limitations. In particular,
our results show that DR cannot provide the solution to the
naturalness/hierarchy problem. The absence of too large corrections to the
Higgs boson mass is due to a secretly realized fine-tuning, rather than special
physical properties of DR. We also investigate these issues within the
Wilsonian RG framework and, by comparison with the usual perturbative RG
analysis, we show that several popular proposals for the resolution of the
problem, commonly considered as physical mechanisms free of fine-tuning, again
secretly implement the tuning. | A Note on Orientifolds and Dualities of Type 0B String Theory: We generalize the construction of four dimensional non-tachyonic orientifolds
of type 0B string theory to non-supersymmetric backgrounds. We construct a four
dimensional model containing self-dual D3 and D9-branes and leading to a chiral
anomaly-free massless spectrum. Moreover, we discuss a further tachyon-free six
dimensional model with only D5 branes. Eventually, we speculate about strong
coupling dual models of the ten-dimensional orientifolds of type 0B. |
Thermodynamics of third order Lovelock adS black holes in the presence
of Born-Infeld type nonlinear electrodynamics: In this paper, we obtain topological black hole solutions of third order
Lovelock gravity couple with two classes of Born-Infeld type nonlinear
electrodynamics with anti-de Sitter asymptotic structure. We investigate
geometric and thermodynamics properties of the solutions and obtain conserved
quantities of the black holes. We examine the first law of thermodynamics and
find that the conserved and thermodynamic quantities of the black hole
solutions satisfy the first law of thermodynamics. Finally, we calculate the
heat capacity and determinant of Hessian matrix to evaluate thermal stability
in both canonical and grand canonical ensembles. Moreover, we consider extended
phase space thermodynamics to obtain generalized first law of thermodynamics as
well as extended Smarr formula. | Odd Scalar Curvature in Anti-Poisson Geometry: Recent works have revealed that the recipe for field-antifield quantization
of Lagrangian gauge theories can be considerably relaxed when it comes to
choosing a path integral measure \rho if a zero-order term \nu_{\rho} is added
to the \Delta operator. The effects of this odd scalar term \nu_{\rho} become
relevant at two-loop order. We prove that \nu_{\rho} is essentially the odd
scalar curvature of an arbitrary torsion-free connection that is compatible
with both the anti-Poisson structure E and the density \rho. This extends a
previous result for non-degenerate antisymplectic manifolds to degenerate
anti-Poisson manifolds that admit a compatible two-form. |
Non-Relativistic BMS algebra: We construct two possible candidates for the non-relativistic
$\mathfrak{bms}_4$ algebra in 4 space-time dimensions by contracting the
original relativistic $\mathfrak{bms}_4$ algebra. The $\mathfrak{bms}_4$
algebra is infinite-dimensional, and it contains the generators of the
Poincar\'e algebra, together with the so-called super-translations. Similarly,
the proposed $\mathfrak{nrbms}_4$ algebras can be regarded as two
infinite-dimensional extensions of the Bargmann algebra. We also study a
canonical realisation of one these algebras in terms of the Fourier modes of a
free Schr\"odinger field, mimicking the canonical realisation of the
relativistic $\mathfrak{bms}_4$ algebra using a free Klein-Gordon field. | Octonionic Gravitational Instantons: We construct eight-dimensional gravitational instantons by solving
appropriate self-duality equations for the spin-connection. The particular
gravitational instanton we present has $Spin(7)$ holonomy and, in a sense, it
is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a
removable bolt singularity which is topologically S^4 and its boundary at
infinity is the squashed S^7. We also lift our solutions to ten and eleven
dimensions and construct fundamental string and membrane configurations that
preserve 1/16 of the original supersymmetries. |
Black Holes as Brains: Neural Networks with Area Law Entropy: Motivated by the potential similarities between the underlying mechanisms of
the enhanced memory storage capacity in black holes and in brain networks, we
construct an artificial quantum neural network based on gravity-like synaptic
connections and a symmetry structure that allows to describe the network in
terms of geometry of a d-dimensional space. We show that the network possesses
a critical state in which the gapless neurons emerge that appear to inhabit a
(d-1)-dimensional surface, with their number given by the surface area. In the
excitations of these neurons, the network can store and retrieve an
exponentially large number of patterns within an arbitrarily narrow energy gap.
The corresponding micro-state entropy of the brain network exhibits an area
law. The neural network can be described in terms of a quantum field, via
identifying the different neurons with the different momentum modes of the
field, while identifying the synaptic connections among the neurons with the
interactions among the corresponding momentum modes. Such a mapping allows to
attribute a well-defined sense of geometry to an intrinsically non-local
system, such as the neural network, and vice versa, it allows to represent the
quantum field model as a neural network. | Stable Solitons in Field Theory Models for Tachyon Condensation: We study soliton solutions in scalar field theory with a variety of unbounded
potentials. A subset of these potentials have Gaussian lump solutions and their
fluctuation spectrum is governed by the harmonic oscillator problem. These
lumps are unstable with one tachyonic mode. Soliton solutions in several other
classes of potentials are stable and are of kink type. The problem of the
stability of these solutions is related to a supersymmetric quantum mechanics
problem. The fluctuation spectrum is not equispaced and does not contain any
tachyonic mode. The lowest energy mode is the massless Goldstone mode which
restores broken translation invariance. |
On the Phenomenology of Tachyon Radiation: We present a brief overview of the different kinds of electromagnetic
radiations expected to come from (or to be induced by) space-like sources
(tachyons). New domains of radiation are here considered; and the possibility
of experimental observation of tachyons via electromagnetic radiation is
discussed. | Cubic interactions of massless higher spins in (A)dS: metric-like
approach: Cubic interactions of higher-spin gauge fields in (A)dS are studied in the
metric-like approach. Making use of the traceless and transverse constraints
together with the ambient-space formalism, all consistent parity-invariant
cubic vertices are obtained for d>3 in closed form pointing out the key role of
their flat-space counterparts. |
The relativistic virial theorem and scale invariance: The virial theorem is related to the dilatation properties of bound states.
This is realized, in particular, by the Landau-Lifshitz formulation of the
relativistic virial theorem, in terms of the trace of the energy-momentum
tensor. We construct a Hamiltonian formulation of dilatations in which the
relativistic virial theorem naturally arises as the condition of stability
against dilatations. A bound state becomes scale invariant in the
ultrarelativistic limit, in which its energy vanishes. However, for very
relativistic bound states, scale invariance is broken by quantum effects and
the virial theorem must include the energy-momentum tensor trace anomaly. This
quantum field theory virial theorem is directly related to the Callan-Symanzik
equations. The virial theorem is applied to QED and then to QCD, focusing on
the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4
of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly. | Inflationary implications of the Covariant Entropy Bound and the
Swampland de Sitter Conjectures: We present a proposal to relate the de Sitter Conjecture (dSC) to the
Covariant Entropy Bound (CEB). By assuming an early phase of accelerated
expansion where the CEB is satisfied, we take into account a contribution from
extra-dimensions to the four-dimensional entropy which restricts the values of
the usual slow-roll parameters. We show in this context that the dSC
inequalities follow from the CEB -- including their mutual exclusion -- in both
single and multi-field inflationary scenarios. We also observe that the order
one constants, c and c' in the conjecture are given in terms of physical
quantities such as the change in entropy over time, the Hubble constant and the
dynamics of the effective scalar fields. Finally, we give a simple example to
illustrate a possible contribution to the four-dimensional entropy from a flux
string scenario. |
At the End of the World: Local Dynamical Cobordism: The Cobordism Conjecture states that any Quantum Gravity configuration
admits, at topological level, a boundary ending spacetime. We study the
dynamical realization of cobordism, as spacetime dependent solutions of
Einstein gravity coupled to scalars containing such end-of-the-world "branes".
The latter appear in effective theory as a singularity at finite spacetime
distance at which scalars go off to infinite field space distance. We provide a
local description near the end-of-the-world branes, in which the solutions
simplify dramatically and are characterized in terms of a critical exponent,
which controls the asymptotic profiles of fields and the universal scaling
relations among the spacetime distance to the singularity, the field space
distance, and the spacetime curvature. The analysis does not rely on
supersymmetry. We study many explicit examples of such Local Dynamical
Cobordisms in string theory, including 10d massive IIA, the 10d
non-supersymmetric $USp(32)$ theory, Bubbles of Nothing, 4d $ \mathcal{N}=1 $
cosmic string solutions, the Klebanov-Strassler throat, D$p$-brane solutions,
brane configurations related to the D1/D5 systems, and small black holes. Our
framework encompasses diverse recent setups in which scalars diverge at the
core of defects, by regarding them as suitable end-of-the-world branes. We
explore the interplay of Local Dynamical Cobordisms with the Distance
Conjecture and other swampland constraints. | Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?: The renormalized entanglement entropy (REE) across a circle of radius R has
been proposed as a c-function in Poincar\'e invariant (2+1)-dimensional field
theory. A proof has been presented of its monotonic behavior as a function of
R, based on the strong subadditivity of entanglement entropy. However, this
proof does not directly establish stationarity of REE at conformal fixed points
of the renormalization group. In this note we study the REE for the free
massive scalar field theory near the UV fixed point described by a massless
scalar. Our numerical calculation indicates that the REE is not stationary at
the UV fixed point. |
Symmetric Ghost Lagrange Densities for the Coupling of Gravity to Gauge
Theories: We derive and present symmetric ghost Lagrange densities for the coupling of
General Relativity to Yang--Mills theories. The graviton-ghost is constructed
with respect to the linearized de Donder gauge fixing and the gauge ghost is
constructed with respect to the covariant Lorenz gauge fixing. Both ghost
Lagrange densities together with their accompanying gauge fixing Lagrange
densities are obtained from the action of the diffeomorphism and gauge BRST and
anti-BRST operators on suitable gauge fixing bosons. In addition, we introduce
a total gauge fixing boson and show that the complete ghost and gauge fixing
Lagrange density can be generated thereof using the total BRST operator and the
total anti-BRST operator, introduced by the author in a previous article
(2022). This generalizes results from Baulieu and Thierry-Mieg (1982) to
General Relativity and covariant Yang--Mills theories. | Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD: We consider N=2 supersymmetric QCD with the gauge group SU(N_c)=SU(N+1) and
N_f number of quark matter multiplets, being perturbed by a small mass term for
the adjoint matter, so that its Coulomb branch shrinks to a number of isolated
vacua. We discuss the vacuum where r=N quarks develop VEV's for N_f\geq
2N=2N_c-2 (in particular, we focus on the N_f= 2N and N_f= 2N+1 cases). In the
equal quark mass limit at large masses this vacuum stays at weak coupling, the
low-energy theory has U(N) gauge symmetry and one observes the non-Abelian
confinement of monopoles. As we reduce the average quark mass and enter the
strong coupling regime the quark condensate transforms into the condensate of
dyons. We show that the low energy description in the strongly-coupled domain
for the original theory is given by U(N) dual gauge theory of N_f\geq 2N light
non-Abelian dyons, where the condensed dyons still cause the confinement of
monopoles, and not of the quarks, as can be thought by naive duality. |
Characters of the W3 algebra: Traces of powers of the zero mode in the W3 Algebra have recently been found
to be of interest, for example in relation to Black Hole thermodynamics, and
arise as the terms in an expansion of the full characters of the algebra. We
calculate the first few such powers in two cases. Firstly, we find the traces
in the 3-state Potts model by using null vectors to derive modular differential
equations for the traces. Secondly, we calculate the exact results for Verma
module representations. We compare our two methods with each other and the
result of brute-force diagonalisation for low levels and find complete
agreement. | $T \bar T$ and EE, with implications for (A)dS subregion encodings: We initiate a study of subregion dualities, entropy, and redundant encoding
of bulk points in holographic theories deformed by $T \bar T$ and its
generalizations. This includes both cut off versions of Anti de Sitter
spacetime, as well as the generalization to bulk de Sitter spacetime, for which
we introduce two additional examples capturing different patches of the bulk
and incorporating the second branch of the square root dressed energy formula.
We provide new calculations of entanglement entropy (EE) for more general
divisions of the system than the symmetric ones previously available. We find
precise agreement between the gravity side and deformed-CFT side results to all
orders in the deformation parameter at large central charge. An analysis of the
fate of strong subadditivity for relatively boosted regions indicates
nonlocality reminiscent of string theory. We introduce the structure of
operator algebras in these systems. The causal and entanglement wedges
generalize to appropriate deformed theories but exhibit qualitatively new
behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads
to subtleties which we express in terms of the Hamiltonian and modular
Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points,
including the cosmological case. |
Duality-Symmetric Three-Brane and its Coupling to Type IIB Supergravity: Starting from the bosonic sector of the M-theory super-five-brane we obtain
the action for duality-symmetric three-brane and construct the consistent
coupling of the proposed action with the bosonic sector of type IIB
supergravity. | Reconstruction of an AdS Radiation/Boson Star Bulk Geometry Using
Light-cone Cuts: Light-cone cuts have recently been proposed as a method to reconstruct the
conformal metric of a holographic spacetime. We explore how additional
information about the bulk geometry gets encoded in the structure of these
light-cone cuts. In particular, we study how the hyperbolic angle related to a
cusp in the light-cone cut encodes information about the matter content of the
spacetime. We provide an explicit numerical example reconstructing the metric
for a 4- dimensional spacetime composed by the superposition of a boson star
and a gas of radiation in AdS. |
Wodzicki residue and anomalies of current algebras: The commutator anomalies (Schwinger terms) of current algebras in $3+1$
dimensions are computed in terms of the Wodzicki residue of pseudodifferential
operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie
algebra of PSDO's. The construction of the (second quantized) current algebra
is closely related to a geometric renormalization of the interaction
Hamiltonian $H_I=j_{\mu} A^{\mu}$ in gauge theory. | Smooth Bosonization as a Quantum Canonical Transformation: We consider a 1+1 dimensional field theory which contains both a complex
fermion field and a real scalar field. We then construct a unitary operator
that, by a similarity transformation, gives a continuum of equivalent theories
which smoothly interpolate between the massive Thirring model and the
sine-Gordon model. This provides an implementation of smooth bosonization
proposed by Damgaard et al. as well as an example of a quantum canonical
transformation for a quantum field theory. |
Exceptional Field Theory II: E$_{7(7)}$: We introduce exceptional field theory for the group E_{7(7)}, based on a
(4+56)-dimensional spacetime subject to a covariant section condition. The
`internal' generalized diffeomorphisms of the coordinates in the fundamental
representation of E_{7(7)} are governed by a covariant `E-bracket', which is
gauged by 56 vector fields. We construct the complete and unique set of field
equations that is gauge invariant under generalized diffeomorphisms in the
internal and external coordinates. Among them feature the non-abelian twisted
self-duality equations for the 56 gauge vectors. We discuss the explicit
solutions of the section condition describing the embedding of the full,
untruncated 11-dimensional and type IIB supergravity, respectively. As a new
feature compared to the previously constructed E_{6(6)} formulation, some
components among the 56 gauge vectors descend from the 11-dimensional dual
graviton but nevertheless allow for a consistent coupling by virtue of a
covariantly constrained compensating 2-form gauge field. | Planckian Axions and the Weak Gravity Conjecture: Several recent works have claimed that the Weak Gravity Conjecture (WGC)
excludes super-Planckian displacements of axion fields, and hence large-field
axion inflation, in the absence of monodromy. We argue that in theories with
$N\gg1$ axions, super-Planckian axion diameters $\cal{D}$ are readily allowed
by the WGC. We clarify the nontrivial relationship between the kinetic matrix
$K$ --- unambiguously defined by its form in a Minkowski-reduced basis --- and
the diameter of the axion fundamental domain, emphasizing that in general the
diameter is not solely determined by the eigenvalues $f_1^2 \le ... \le f_N^2$
of $K$: the orientations of the eigenvectors with respect to the
identifications imposed by instantons must be incorporated. In particular, even
if one were to impose the condition $f_N<M_{pl}$, this would imply neither
${\cal D}<M_{pl}$ nor ${\cal D}<\sqrt{N}M_{pl}$. We then estimate the actions
of instantons that fulfill the WGC. The leading instanton action is bounded
from below by $S \ge {\cal S} M_{pl}/f_N$, with ${\cal S}$ a fixed constant,
but in the universal limit $S\gtrsim {\cal S} \sqrt{N}M_{pl}/f_N$. Thus, having
$f_N>M_{pl}$ does not immediately imply the existence of unsuppressed higher
harmonic contributions to the potential. Finally, we argue that in effective
axion-gravity theories, the zero-form version of the WGC can be satisfied by
gravitational instantons that make negligible contributions to the potential. |
Generalised cosmology of codimension-two braneworlds: It has recently been argued that codimension-two braneworlds offer a
promising line of attack on the cosmological constant problem, since in such
models the Hubble rate is not directly related to the brane tension. We point
out challenges to building more general models where the brane content is not
restricted to pure tension. In order to address these challenges, we construct
a thick brane model which we linearize around a well known static solution. We
show that the model's cosmology does reduce to standard FRW behaviour, but find
no hint of a self-tuning mechanism which might help solve the cosmological
constant problem whithin the context of non-supersymmetric Einstein gravity. | Conformal Correlators on the Lorentzian Torus: The general form of a 2D conformal field theory (CFT) correlator on a
Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is
well-known. This paper describes the general form of 2- and 3-point CFT
correlators on the Lorentzian torus $\mathcal{LT}^2$ which arises as the
conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R})$ $\simeq
\text{AdS}_3/\mathbb{Z}$. We consider only generic points, thereby omitting an
analysis of contact terms, which already exhibits a surprisingly rich
structure. The results are relevant to celestial holography, for which the
$\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative
celestial CFT. |
Algorithmic derivation of functional renormalization group equations and
Dyson-Schwinger equations: We present the Mathematica application DoFun which allows to derive
Dyson-Schwinger equations and renormalization group flow equations for n-point
functions in a simple manner. DoFun offers several tools which considerably
simplify the derivation of these equations from a given physical action. We
discuss the application of DoFun by means of two different types of quantum
field theories, namely a bosonic O(N) theory and the Gross-Neveu model. | T-duality in the weakly curved background: We consider the closed string propagating in the weakly curved background
which consists of constant metric and Kalb-Ramond field with infinitesimally
small coordinate dependent part. We propose the procedure for constructing the
T-dual theory, performing T-duality transformations along coordinates on which
the Kalb-Ramond field depends. The obtained theory is defined in the
non-geometric double space, described by the Lagrange multiplier $y_\mu$ and
its $T$-dual $\tilde{y}_\mu$. We apply the proposed T-duality procedure to the
T-dual theory and obtain the initial one. We discuss the standard relations
between T-dual theories that the equations of motion and momenta modes of one
theory are the Bianchi identities and the winding modes of the other. |
Massive Degeneracy and Goldstone Bosons: A Challenge for the Light Cone: Wherein it is argued that the light front formalism has problems dealing with
Goldstone symmetries. It is further argued that the notion that in hadron
condensates can explain Goldstone phenomena is false. | Subleading Microstate Counting in the Dual to Massive Type IIA: We study the topologically twisted index of a certain Chern-Simons matter
theory with $SU(N)$ level $k$ gauge group on a genus $g$ Riemann surface times
a circle. For this theory it is known that the logarithm of the topologically
twisted index grows as $N^{5/3}$ and that it matches the Bekenstein-Hawking
entropy of certain magnetically charged asymptotically $AdS_4\times S^6$ black
holes in massive type IIA supergravity. Through a combination of numerical and
analytical techniques we study the subleading in $N$ structure. We demonstrate
precise analytic cancellation of terms of orders $N\log\,N$ and $N^{1/3}\log N$
and show numerical cancellation for terms of order $N$. As a result, the first
subleading correction is of order $N^{2/3}$. Furthermore, we provide evidence
for the presence of a term of the form $(g-1)(7/18) \log \,N$ which constitutes
a microscopic prediction for the one-loop contribution coming from the massless
gravitational degrees of freedom in the massive IIA black hole. |
Weyl's Gauge Invariance: Conformal Geometry, Spinors, Supersymmetry, and
Interactions: We extend our program, of coupling theories to scale in order to make their
Weyl invariance manifest, to include interacting theories, fermions and
supersymmetric theories. The results produce mass terms coinciding with the
standard ones for universes that are Einstein, but are novel in general
backgrounds. They are generalizations of the gravitational couplings of a
conformally improved scalar to fields with general scaling and tensor
properties. The couplings we find are more general than just trivial ones
following from the conformal compensating mechanisms. In particular, in the
setting where a scale gauge field (or dilaton) is included, masses correspond
to Weyl weights of fields organized in ``tractor'' multiplets.
Breitenlohner--Freedman bounds follow directly from reality of these weights.
Moreover, massive, massless and partially massless theories are handled in a
uniform framework. Also, bona fide Weyl invariant theories (invariant without
coupling to scale) can be directly derived in this approach. The results are
based on the tractor calculus approach to conformal geometry, in particular we
show how to handle fermi fields, supersymmetry and Killing spinors using
tractor techniques. Another useful consequence of the construction is that it
automatically produces the (anti) de Sitter theories obtained by log-radial
reduction of Minkowski theories in one higher dimension. Theories presented in
detail include interacting scalars, spinors, Rarita--Schwinger fields, and the
interacting Wess--Zumino model. | Conformally covariant operators of mixed-symmetry tensors and MAGs: We compute conformally covariant actions and operators for tensors with mixed
symmetries in arbitrary dimension $d$. Our results complete the classification
of conformal actions that are quadratic on arbitrary tensors with three
indices, which allows to write corresponding conformal actions for all tensor
species that appear in the decomposition of the distorsion tensor of an
arbitrary metric-affine theory of gravity including both torsion and
nonmetricity. We also discuss the degrees of freedom that such theories are
propagating, as well as interacting metric-affine theories that enjoy the
conformal actions in the Gaussian limit. |
S-fold magnetic quivers: Magnetic quivers and Hasse diagrams for Higgs branches of rank $r$ 4d
$\mathcal{N}=2$ SCFTs arising from $\mathbb{Z}_{\ell}$ $\mathcal{S}$-fold
constructions are discussed. The magnetic quivers are derived using three
different methods: 1) Using clues like dimension, global symmetry, and the
folding parameter $\ell$ to guess the magnetic quiver. 2) From 6d
$\mathcal{N}=(1,0)$ SCFTs as UV completions of 5d marginal theories, and
specific FI deformations on their magnetic quiver, which is further folded by
$\mathbb{Z}_{\ell}$. 3) From T-duality of Type IIA brane systems of 6d
$\mathcal{N}=(1,0)$ SCFTs and explicit mass deformation of the resulting brane
web followed by $\mathbb{Z}_{\ell}$ folding. A choice of the ungauging scheme,
either on a long node or on a short node, yields two different moduli spaces
related by an orbifold action, thus suggesting a larger set of SCFTs in four
dimensions than previously expected. | Conformal internal symmetry of $2d$ $σ$-models coupled to gravity
and a dilaton: General Relativity reduced to two dimensions possesses a large group of
symmetries that exchange classical solutions. The associated Lie algebra is
known to contain the affine Kac-Moody algebra $A_1^{(1)}$ and half of a real
Witt algebra. In this paper we exhibit the full symmetry under the semi-direct
product of $\Lie{A_1^{(1)}}$ by the Witt algebra $\Lie{\Wir}$. Furthermore we
exhibit the corresponding hidden gauge symmetries. We show that the theory can
be understood in terms of an infinite dimensional potential space involving all
degrees of freedom: the dilaton as well as matter and gravitation. In the
dilaton sector the linear system that extends the previously known Lax pair has
the form of a twisted self-duality constraint that is the analog of the
self-duality constraint arising in extended supergravities in higher spacetime
dimensions. Our results furnish a group theoretical explanation for the
simultaneous occurrence of two spectral parameters, a constant one ($=y$) and a
variable one ($=t$). They hold for all $2d$ non-linear $\sigma$-models that are
obtained by dimensional reduction of $G/H$ models in three dimensions coupled
to pure gravity. In that case the Lie algebra is $\Lie{\Wir \semi G^{(1)}}$;
this symmetry acts on a set of off shell fields (in a fixed gauge) and
preserves the equations of motion. |
Fundamental Strings as Noncommutative Solitons: The interpretation of closed fundamental strings as solitons in open string
field theory is reviewed. Noncommutativity is introduced to facilitate an
explicit construction. The tension is computed exactly and the correct spectrum
is recovered at long wave length. | String Field Theory -- A Modern Introduction: This book provides an introduction to string field theory (SFT). String
theory is usually formulated in the worldsheet formalism, which describes a
single string (first-quantization). While this approach is intuitive and could
be pushed far due to the exceptional properties of two-dimensional theories, it
becomes cumbersome for some questions or even fails at a more fundamental
level. These motivations have led to the development of SFT, a description of
string theory using the field theory formalism (second-quantization). As a
field theory, SFT provides a rigorous and constructive formulation of string
theory.
The main objective is to construct the closed bosonic SFT and to explain how
to assess the consistency of string theory with it. The accent is put on
providing the reader with the foundations, conceptual understanding and
intuition of what SFT is. After reading this book, they should be able to study
the applications from the literature.
The book is organized in two parts. The first part reviews the topics of the
worldsheet theory that are necessary to build SFT (worldsheet path integral,
CFT and BRST quantization). The second part starts by introducing general
concepts of SFT from the BRST quantization. Then, it introduces off-shell
string amplitudes before providing a Feynman diagrams interpretation from which
the building blocks of SFT are extracted. After constructing the closed SFT, it
is used to outline the proofs of several important consistency properties, such
as background independence, unitarity and crossing symmetry. Finally, the
generalization to the superstring is also discussed.
This book grew up from lecture notes for a course given at the
Ludwig-Maximilians-Universit\"at LMU (winter semesters 2017-2018 and
2018-2019). The current document is the draft of the manuscript published by
Springer. |
A Computer Test of Holographic Flavour Dynamics: We perform computer simulations of the Berkooz-Douglas (BD) matrix model,
holographically dual to the D0/D4-brane intersection. We generate the
fundamental condensate versus bare mass curve of the theory both
holographically and from simulations of the BD model. Our studies show
excellent agreement of the two approaches in the deconfined phase of the theory
and significant deviations in the confined phase. We argue the discrepancy in
the confined phase is explained by the embedding of the D4-brane which yields
stronger $\alpha'$ corrections to the condensate in this phase. | Light-by-Light Scattering Effect in Light-Cone Supergraphs: We give a relatively simple explanation of the light-cone supergraph
prediction for the UV properties of the maximally supersymmetric theories. It
is based on the existence of a dynamical supersymmetry which is not manifest in
the light-cone supergraphs. It suggests that N=4 supersymmetric Yang-Mills
theory is UV finite and N=8 supergravity is UV finite at least until 7 loops
whereas the $n$-point amplitudes have no UV divergences at least until $L=n+3$.
Here we show that this prediction can be deduced from the properties of
light-cone supergraphs analogous to the light-by-light scattering effect in
QED. A technical aspect of the argument relies on the observation that the
dynamical supersymmetry action is, in fact, a compensating field-dependent
gauge transformation required for the retaining the light-cone gauge condition
$A_+=0$. |
On Mass Spectrum in SQCD. Unequal quark masses: N=1 SQCD with N_c colors and two types of light quarks: N_l flavors with
smaller masses m_l and N_h=N_F-N_l flavors with larger masses m_h,
N_c<N_F<3N_c, 0<m_l \leq m_h \ll \Lambda, is considered within the dynamical
scenario in which quarks can form the coherent colorless diquark-condensate.
There are several phase states at different values of parameters r=m_l/m_h,
N_l, and N_F. Properties of these phases and the mass spectra therein are
described. | Color structures and permutations: Color structures for tree level scattering amplitudes in gauge theory are
studied in order to determine the symmetry properties of the color-ordered
sub-amplitudes. We mathematically formulate the space of color structures
together with the action of permuting external legs. The character generating
functions are presented from the mathematical literature and we determine the
decomposition into irreducible representations. Mathematically, free Lie
algebras and the Lie operad are central. A study of the implications for
sub-amplitudes is initiated and we prove directly that both the Parke-Taylor
amplitudes and Cachazo-He-Yuan amplitudes satisfy the Kleiss-Kuijf relations. |
Semiclassical corrections to black hole entropy and the generalized
uncertainty principle: In this paper, employing the path integral method in the framework of a
canonical description of a Schwarzschild black hole, we obtain the corrected
inverse temperature and entropy of the black hole. The corrections are those
coming from the quantum effects as well as from the Generalized Uncertainty
Principle effects. Furthermore, an equivalence between the polymer quantization
and the Generalized Uncertainty Principle description is shown provided the
parameters characterizing these two descriptions are proportional. | Polynomial Form Factors in the O(3) Nonlinear sigma-Model: We study the general structure of Smirnov's axioms on form factors of local
operators in integrable models. We find various consistency conditions that the
form factor functions have to satisfy. For the special case of the $O(3)$
$\sigma$-model we construct simple polynomial solutions for the operators of
the spin-field, current, energy-momentum tensor and topological charge density. |
A New Derivation of the Picard-Fuchs Equations for Effective $N = 2$
Super Yang-Mills Theories: A new method to obtain the Picard-Fuchs equations of effective $N = 2$
supersymmetric gauge theories in 4 dimensions is developed. It includes both
pure super Yang-Mills and supersymmetric gauge theories with massless matter
hypermultiplets. It applies to all classical gauge groups, and directly
produces a decoupled set of second-order, partial differential equations
satisfied by the period integrals of the Seiberg-Witten differential along the
1-cycles of the algebraic curves describing the vacuum structure of the
corresponding $N = 2$ theory. | Superstrings on AdS_5 x S^5 supertwistor space: We derive the Green-Schwarz action on AdS_5 x S^5 using an alternate version
of the coset superspace construction. By Wick rotations and Lie algebra
identifications we bring the coset to GL(4|4)/(Sp(4) x GL(1))^2, which allows
us to represent the conformal transformations on unconstrained matrices. The
derivation is more streamlined even for the bosonic sector, and conformal
symmetry is manifest at every step. Kappa-symmetry gauge fixing is more
transparent. |
Deformation Quantization and Wigner Functions: We review the Weyl-Wigner formulation of quantum mechanics in phase space. We
discuss the concept of Narcowich-Wigner spectrum and use it to state necessary
and sufficient conditions for a phase space function to be a Wigner
distribution. Based on this formalism we analize the modifications introduced
by the presence of boundaries. Finally, we discuss the concept of
environment-induced decoherence in the context of the Weyl-Wigner approach. | Solitons in Brane Worlds II: We study the solution describing a non-extreme dilatonic (p+1)-brane
intersecting a D-dimensional extreme dilatonic domain wall, where one of its
longitudinal directions is along the direction transverse to the domain wall,
in relation to the Randall-Sundrum type model. The dynamics of the probe
(p+1)-brane in such source background reproduces that of the probe p-brane in
the background of the (D-1)-dimensional source p-brane. However, as for a probe
test particle, the dynamics in one lower dimensions is reproduced, only when
the source (p+1)-brane is uncharged. |
Topics in Two-Loop Superstring Perturbation Theory: In this contribution to the Proceedings of the Conference on Analysis,
Complex Geometry, and Mathematical Physics, an expository overview of
superstring perturbation theory to two loop order is presented to an audience
of mathematicians and physicists. Recent results on perturbative supersymmetry
breaking effects in Heterotic string theory compactified on Z_2 \times Z_2
Calabi-Yau orbifolds, and the calculation of the two-loop vacuum energy in
these theories are discussed in detail, and the appearance of a new modular
identity with respect to Sp(4,Z)/Z_4 is reviewed. | Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\
$ symmetry: We show how two-dimensional incompressible quantum fluids and their
excitations can be viewed as $\ W_{1+\infty}\ $ edge conformal field theories,
thereby providing an algebraic characterization of incompressibility. The
Kac-Radul representation theory of the $\ W_{1+\infty}\ $ algebra leads then to
a purely algebraic complete classification of hierarchical quantum Hall states,
which encompasses all measured fractions. Spin-polarized electrons in
single-layer devices can only have Abelian anyon excitations. |
Quark Masses from Gaugino Condensation in String Theories: We present a mechanism able to generate the perturbatively absent up/down
$<{\bf 10} \cdot {\bf 10} \cdot {\bf 5}^H>$ quark Yukawa couplings of
SU(5)/flipped SU(5) GUTS in Type II orientifold compactifications with
D-branes. The mechanism works when there are Sp(N) gauge groups involved. The
${\bf {\bar 5}}$'s get charged under the Sp(N) gauge groups and the generation
of quark masses proceeds via the generation of the fermionic Sp(N) singlet
condensate $<{\bf {\bar 5} \cdot {\bar 5} \cdot {\bar 5} \cdot {\bar 5}}>$ in
the term $(1/{M_s^5}) {\bf 10} \cdot {\bf 10} \cdot < {\bf {\bar 5} \cdot {\bar
5} \cdot {\bar 5} \cdot {\bar 5}}>$. Also non-chiral states charged under Sp
gauge groups may become constrained by the requirement of Sp's becoming
strongly coupled. | The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass
gap and confinement problems: Using generalized Konishi anomaly equations, it is known that one can
express, in a large class of supersymmetric gauge theories, all the chiral
operators expectation values in terms of a finite number of a priori arbitrary
constants. We show that these constants are fully determined by the requirement
of gauge invariance and an additional anomaly equation. The constraints so
obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa
quantum glueball superpotential, with all terms (including the
Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill
non-trivial gaps in existing derivations of the mass gap and confinement
properties in super Yang-Mills theories. |
Diagrammatics of a colored SYK model and of an SYK-like tensor model,
leading and next-to-leading orders: The Sachdev-Ye-Kitaev (SYK) model is a model of $q$ interacting fermions.
Gross and Rosenhaus have proposed a generalization of the SYK model which
involves fermions with different flavors. In terms of Feynman graphs, those
flavors are reminiscent of the colors used in random tensor theory. This gives
us the opportunity to apply some modern, yet elementary, tools developed in the
context of random tensors to one particular instance of such colored SYK
models. We illustrate our method by identifying all diagrams which contribute
to the leading and next-to-leading orders of the 2-point and 4-point functions
in the large $N$ expansion, and argue that our method can be further applied if
necessary. In a second part we focus on the recently introduced Gurau-Witten
tensor model and also extract the leading and next-to-leading orders of the
2-point and 4-point functions. This analysis turns out to be remarkably more
involved than in the colored SYK model. | Gravitational Dressing of Aharonov-Bohm Amplitudes: We investigate Aharonov-Bohm scattering in a theory in which charged bosonic
matter fields are coupled to topologically massive electrodynamics and
topologically massive gravity. We demonstrate that, at one-loop order, the
transmuted spins in this theory are related to the ones of ordinary
Chern-Simons gauge theory in the same way that the
Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal
weights of primary operators to the bare weights in two-dimensional conformal
field theories. We remark on the implications of this connection between
two-dimensional conformal field theories and three-dimensional gauge and
gravity theories for a topological membrane reformulation of strings. We also
discuss some features of the gravitational analog of the Aharonov-Bohm effect. |
Information Retrieval from a Charge `Trap': We study the model of massless $1+1$ electrodynamics with nonconstant
coupling, introduced by Peet, Susskind and Thorlacius as the `charge hole'. But
we take the boundary of the strong coupling region to be first timelike, then
spacelike for a distance $X$, and then timelike again (to mimic the structure
of a black hole). For an incident charge pulse entering this `charge trap' the
charge and information get separated. The charge comes out near the endpoint of
the singularity. The `information' travels a well localised path through the
strong coupling region and comes out later. | Machine Learning CICY Threefolds: The latest techniques from Neural Networks and Support Vector Machines (SVM)
are used to investigate geometric properties of Complete Intersection
Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model
building. An advanced neural network classifier and SVM are employed to (1)
learn Hodge numbers and report a remarkable improvement over previous efforts,
(2) query for favourability, and (3) predict discrete symmetries, a highly
imbalanced problem to which both Synthetic Minority Oversampling Technique
(SMOTE) and permutations of the CICY matrix are used to decrease the class
imbalance and improve performance. In each case study, we employ a genetic
algorithm to optimise the hyperparameters of the neural network. We demonstrate
that our approach provides quick diagnostic tools capable of shortlisting
quasi-realistic string models based on compactification over smooth CICYs and
further supports the paradigm that classes of problems in algebraic geometry
can be machine learned. |
Quantum Field Theory: Spin Zero: This is a draft version of Part I of a three-part textbook on quantum field
theory. | On type 0 string theory in solvable RR backgrounds: Motivated by a possibility of solving non-supersymmetric type 0 string theory
in $AdS_5 \times S^5$ background using integrability, we revisit the
construction of type 0 string spectrum in some solvable examples of backgrounds
with RR fluxes that are common to type IIB and type 0B theories. The presence
of RR fluxes requires the use of a Green-Schwarz description for type 0 string
theory. Like in flat space, the spectrum of type 0 theory can be derived from
the type II theory spectrum by a $(-1)^F$ orbifolding, i.e. combining the
untwisted sector where GS fermions are periodic with the twisted sector where
GS fermions are antiperiodic (and projecting out all spacetime fermionic
states). This construction of the type 0 spectrum may also be implemented using
a Melvin background that allows to continuously interpolate between the type II
and type 0 theories. As an illustration, we discuss the type 0B spectrum in the
pp-wave background which is the Penrose limit of $AdS_5 \times S^5$ with RR
5-form flux and also in the pp-wave background which is the Penrose limit of
$AdS_3 \times S^3 \times T^4$ supported by mixed RR and NSNS 3-form fluxes. We
show that increasing the strength of the RR flux increases the value of the
effective normal ordering constant (which determines the mass of the type 0
tachyon) and thus effectively decreases the momentum-space domain of
instability of the ground state. We also comment on the semiclassical sector of
states of type 0B theory in $AdS_5 \times S^5$. |
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