pinecone/core-2020-05-10-deduplication huggingface dataset:
Painlev\'e VI connection problem and monodromy of c=1 conformal blocks

Generic c=1 four-point conformal blocks on the Riemann sphere can be seen as
the coefficients of Fourier expansion of the tau function of Painlev\'e VI
equation with respect to one of its integration constants. Based on this
relation, we show that c=1 fusion matrix essentially coincides with the
connection coefficient relating tau function asymptotics at different critical
points. Explicit formulas for both quantities are obtained by solving certain
functional relations which follow from the tau function expansions. The final
result does not involve integration and is given by a ratio of two products of
Barnes G-functions with arguments expressed in terms of conformal
dimensions/monodromy data. It turns out to be closely related to the volume of
hyperbolic tetrahedron.Comment: 26 pages, 4 figure
An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and
  Relativistic and Elliptized Integrable Systems

We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d
AGT correspondence for SU(N) -- which essentially relates the relevant 5d and
6d Nekrasov instanton partition functions to the integrable representations of
a q-deformed and elliptic affine W_N-algebra -- can be derived, purely
physically, from the principle that the spacetime BPS spectra of string-dual
M-theory compactifications ought to be equivalent. Via an appropriate defect,
we also derive a "fully-ramified" version of the 5d and 6d AGT correspondence
where integrable representations of a quantum and elliptic affine SU(N)-algebra
at the critical level appear on the 2d side, and argue that the relevant
"fully-ramified" 5d and 6d Nekrasov instanton partition functions are
simultaneous eigenfunctions of commuting operators which define relativistic
and elliptized integrable systems. As an offshoot, we also obtain various
mathematically novel and interesting relations involving the double loop
algebra of SU(N), elliptic Macdonald operators, equivariant elliptic genus of
instanton moduli space, and more.Comment: 53 pages (inclusive of essential review material from
  arXiv:1301.1977). Minor change in (3.22
New Examples of Flux Vacua

Type IIB toroidal orientifolds are among the earliest examples of flux vacua.
By applying T-duality, we construct the first examples of massive IIA flux
vacua with Minkowski space-times, along with new examples of type IIA flux
vacua. The backgrounds are surprisingly simple with no four-form flux at all.
They serve as illustrations of the ingredients needed to build type IIA and
massive IIA solutions with scale separation. To check that these backgrounds
are actually solutions, we formulate the complete set of type II supergravity
equations of motion in a very useful form that treats the R-R fields
democratically.Comment: 38 pages, LaTeX; references updated; additional minor comments added;
  published versio
Unquenched massive flavors and flows in Chern-Simons matter theories

We construct a holographic dual to the three-dimensional ABJM Chern-Simons
matter theory with unquenched massive flavors. The flavor degrees of freedom
are introduced by means of D6-branes extended along the gauge theory directions
and delocalized in the internal space. To find the solution we have to solve
the supergravity equations of motion with the source terms introduced by the
D6-branes. The background we get is a running solution representing the
renormalization group flow between two fixed points, at the IR and the UV, in
both of which the geometry is of the form AdS_4 x M_6, where M_6 is a
six-dimensional compact manifold. Along the flow, N=1 supersymmetry is
preserved and the flavor group is Abelian. The flow is generated by changing
the quark mass m_q. When m_q is very large we recover the original unflavored
ABJM solution, while for m_q very small our solution becomes asymptotically
equivalent to the one found recently for massless smeared flavors. We study the
effects of the dynamical quarks as their mass is varied on different
observables, such as the holographic entanglement entropy, the quark-antiquark
potential, the two-point functions of high dimension bulk operators, and the
mass spectrum of mesons.Comment: 44 pages plus appendices, 11 figures;v2: minor corrections,
  references adde
Spectral dualities in XXZ spin chains and five dimensional gauge
  theories

Motivated by recent progress in the study of supersymmetric gauge theories we
propose a very compact formulation of spectral duality between XXZ spin chains.
The action of the quantum duality is given by the Fourier transform in the
spectral parameter. We investigate the duality in various limits and, in
particular, prove it for q-->1, i.e. when it reduces to the XXX/Gaudin duality.
We also show that the universal difference operators are given by the normal
ordering of the classical spectral curves.Comment: 9 pages, minor corrections, reference adde
3d Chern-Simons Theory from M5-branes

We study 5d N=2 maximally supersymmetric Yang-Mills theory with a gauge group
G on S^2 x M_3, where M_3 is a 3-manifold. By explicit localization computation
we show that the path-integral of the 5d N=2 theory reduces to that of the 3d
G_C Chern-Simons theory on M_3, where G_C is the complexification of G. This
gives a direct derivation of the appearance of the Chern-Simons theory from the
compactification of the 6d (2,0) theory, confirms the predictions from the
3d/3d correspondence for G=SU(N), and suggests the generalization of the
correspondence to more general gauge groups.Comment: 28 pages, minor corrections and references added, comments on the
  gauge-fixing added. The version published in JHE
A Holographic Study on Vector Condensate Induced by a Magnetic Field

We study a holographic model with vector condensate by coupling the anti-de
Sitter gravity to an Abelian gauge field and a charged vector field in $(3+1)$
dimensional spacetime. In this model there exists a non-minimal coupling of the
vector filed to the gauge field. We find that there is a critical temperature
below which the charged vector condenses via a second order phase transition.
The DC conductivity becomes infinite and the AC conductivity develops a gap in
the condensed phase. We study the effect of a background magnetic field on the
system. It is found that the background magnetic field can induce the
condensate of the vector field even in the case without chemical
potential/charge density. In the case with non-vanishing charge density, the
transition temperature raises with the applied magnetic field, and the
condensate of the charged vector operator forms a vortex lattice structure in
the spatial directions perpendicular to the magnetic field.Comment: v3: minor changes, references added, to appear in JHE
Gauge Coupling Unification in E6 F-Theory GUTs with Matter and Bulk
  Exotics from Flux Breaking

We consider gauge coupling unification in E6 F-Theory Grand Unified Theories
(GUTs) where E6 is broken to the Standard Model (SM) gauge group using fluxes.
In such models there are two types of exotics that can affect gauge coupling
unification, namely matter exotics from the matter curves in the 27 dimensional
representation of E6 and the bulk exotics from the adjoint 78 dimensional
representation of E6. We explore the conditions required for either the
complete or partial removal of bulk exotics from the low energy spectrum. In
the latter case we shall show that (miraculously) gauge coupling unification
may be possible even if there are bulk exotics at the TeV scale. Indeed in some
cases it is necessary for bulk exotics to survive to the TeV scale in order to
cancel the effects coming from other TeV scale matter exotics which would by
themselves spoil gauge coupling unification. The combination of matter and bulk
exotics in these cases can lead to precise gauge coupling unification which
would not be possible with either type of exotics considered by themselves. The
combination of matter and bulk exotics at the TeV scale represents a unique and
striking signature of E6 F-theory GUTs that can be tested at the LHC.Comment: 21 pages, 5 figure
Old-minimal supergravity models of inflation

We study three types of the old-minimal higher-derivative supergravity
theories extending the $f(R)$ gravity, towards their use for the inflationary
model building in supergravity, by using both superfields and their field
components. In the curved superspace all those theories are described in terms
of a single chiral scalar curvature superfeld $\mathcal{R}$. Each of those
theories can be dualized into a matter-coupled supergravity without higher
derivatives. The first type is parametrized by a single non-holomorphic
potential $N(\mathcal{R},\bar{\mathcal{R}})$, and gives rise to the dual
matter-coupled supergravities with two dynamical chiral matter superfields
having a no-scale K\"ahler potential. We find that a generic potential
$N(\mathcal{R},\bar{\mathcal{R}})$ generates both the $(R+R^2)$ gravity and the
non-minimal coupling of the propagating complex scalar field to the $R$, needed
for the Starobinsky and Higgs inflation, respectively. We find the general
conditions for the Starobinsky inflation and compute the inflaton mass. The
second type is given by the chiral supergravity actions whose superfield
Lagrangian $F(\mathcal{R},\Sigma({\bar{\mathcal R}}))$ also depends upon the
chiral projection $\Sigma$ of the anti-chiral superfield ${\bar{\mathcal R}}$.
We find that the actions of the second type always give rise to ghosts. We also
revisit the $F(\mathcal{R})$ supergravity actions of the third type (without
the $\Sigma$-dependence) with the reduced number of the extra physical degrees
of freedom, comprising a single chiral matter superfeld with a no-scale
K\"ahler potential. We confirm that the pure $F(\mathcal{R})$ supergravity is
insufficient for realization of the Starobinsky inflation, though by the reason
different from those proposed in the recent literature.Comment: LaTeX, 24 pages, no pictures; Sections 3 and 4 expanded, references
  added, typos correcte
Gauge-Stringy Instantons in N=2 U(N) Gauge Theories

Using D3/D(-1) brane set-up in type IIB string theory we introduce
gauge-stringy instantons in N=2 U(N) supersymmetry theories with one matter
multiplet in symmetric representation. In addition to the gauge and stringy
moduli there exist extra zero modes that we refer to as "gauge-stringy" moduli.
We show that the measure of the moduli space in this model becomes
dimensionless for arbitary N when the gauge instanton charge k_g is equal to
the stringy instanton charge k_s. This property of gauge-stringy instantons
leads to having equal contributions from all instanton charges k_s=k_g=k in the
effective action. We derive the gauge-stringy instanton partition function and
calculate the corrections to the prepotential due to k=1,2 gauge-stringy
instanton charges. As a by-product the partition function for gauge k-instanton
is obtained which coincides with the result from the standard ADHM
construction.Comment: 4 references added, A paragraph added in Conclusions, To appear in
  JHE
Vacuum Bubbles in the Presence of a Relativistic Fluid

First order phase transitions are characterized by the nucleation and
evolution of bubbles. The dynamics of cosmological vacuum bubbles, where the
order parameter is independent of other degrees of freedom, are well known;
more realistic phase transitions in which the order parameter interacts with
the other constituents of the Universe is in its infancy. Here we present
high-resolution lattice simulations that explore the dynamics of bubble
evolution in which the order parameter is coupled to a relativistic fluid. We
use a generic, toy potential, that can mimic physics from the GUT scale to the
electroweak scale.Comment: 9 Pages, 4 Figure
Next-to-leading order electroweak corrections to pp -> W+W- -> 4 leptons
  at the LHC in double-pole approximation

We present the calculation of next-to-leading-order electroweak corrections
to W-boson pair production at the LHC, taking off-shell effects of the W bosons
and their leptonic decays into account in the framework of the so-called
double-pole approximation. In detail, the lowest-order cross section and the
photonic bremsstrahlung are based on full matrix elements with four-fermion
final states, but the virtual one-loop corrections are approximated by the
leading contributions of a systematic expansion about the resonance poles of
the two W bosons. This expansion classifies the virtual corrections into
factorizable and non-factorizable corrections, the calculation of which is
described in detail. Corrections induced by photons in the initial state, i.e.
photon-photon and quark-photon collision channels, are included and based on
complete matrix elements as well. Our numerical results, which are presented
for realistic acceptance cuts applied to the W-boson decay products,
qualitatively confirm recent results obtained for on-shell W bosons and reveal
electroweak corrections of the size of tens of percent in the TeV range of
transverse momenta and invariant masses. In general, photon-photon and
quark-photon induced contributions amount to 5-10% of the full differential
result. Compared to previous predictions based on stable W bosons electroweak
corrections, however, can change by several percent because of realistic cuts
on the W-boson decay products and corrections to the decays.Comment: 35 pages, 10 figure
A Two-Loop Five-Gluon Helicity Amplitude in QCD

We compute the planar part of the two-loop five gluon amplitude with all
helicities positive. To perform the calculation we develop a D-dimensional
generalized unitarity procedure allowing us to reconstruct the amplitude by
cutting into products of six-dimensional trees. We find a compact form for the
integrand which only requires topologies with six or more propagators. We
perform cross checks of the universal infra-red structure using numerical
integration techniques.Comment: 31 pages, 7 figures. version 2 - fix typos and match with journal
  versio
Direct derivation of "mirror" ABJ partition function

We study the partition function of the three-dimensional N=6 U(N)_k x
U(N+M)_{-k} superconformal Chern-Simons matter theory known as the ABJ theory.
We prove that the ABJ partition function on S^3 is exactly the same as a
formula recently proposed by Awata, Hirano and Shigemori. While this formula
was previously obtained by an analytic continuation from the L(2,1) lens space
matrix model, we directly derive this by using a generalization of the Cauchy
determinant identity. We also give an interpretation for the formula from brane
picture.Comment: 12 pages, no figure; v2: minor corrections, references added; v3:
  typos correcte
Chemical potentials in three-dimensional higher spin anti-de Sitter
  gravity

We indicate how to introduce chemical potentials for higher spin charges in
higher spin anti-de Sitter gravity in a manner that manifestly preserves the
original asymptotic W-symmetry. This is done by switching on a non-vanishing
component of the connection along the temporal (thermal) circles. We first
recall the procedure in the pure gravity case (no higher spin) where the only
"chemical potentials" are the temperature and the chemical potential associated
with the angular momentum. We then generalize to the higher spin case. We find
that there is no tension with the W(N) or W(infinity) asymptotic algebra, which
is obviously unchanged by the introduction of the chemical potentials. Our
argument is non-perturbative.Comment: Minor misprints correcte
Hexagon functions and the three-loop remainder function

We present the three-loop remainder function, which describes the scattering
of six gluons in the maximally-helicity-violating configuration in planar N=4
super-Yang-Mills theory, as a function of the three dual conformal cross
ratios. The result can be expressed in terms of multiple Goncharov
polylogarithms. We also employ a more restricted class of "hexagon functions"
which have the correct branch cuts and certain other restrictions on their
symbols. We classify all the hexagon functions through transcendental weight
five, using the coproduct for their Hopf algebra iteratively, which amounts to
a set of first-order differential equations. The three-loop remainder function
is a particular weight-six hexagon function, whose symbol was determined
previously. The differential equations can be integrated numerically for
generic values of the cross ratios, or analytically in certain kinematics
limits, including the near-collinear and multi-Regge limits. These limits allow
us to impose constraints from the operator product expansion and multi-Regge
factorization directly at the function level, and thereby to fix uniquely a set
of Riemann-zeta-valued constants that could not be fixed at the level of the
symbol. The near-collinear limits agree precisely with recent predictions by
Basso, Sever and Vieira based on integrability. The multi-Regge limits agree
with the factorization formula of Fadin and Lipatov, and determine three
constants entering the impact factor at this order. We plot the three-loop
remainder function for various slices of the Euclidean region of positive cross
ratios, and compare it to the two-loop one. For large ranges of the cross
ratios, the ratio of the three-loop to the two-loop remainder function is
relatively constant, and close to -7.Comment: 103 pages, 12 figures, 9 ancillary files. v2: typos corrected,
  references adde
Holographic Phases of Renyi Entropies

We consider Renyi entropies of conformal field theories in flat space, with
the entangling surface being a sphere. The AdS/CFT correspondence relates this
Renyi entropy to that of a black hole with hyperbolic horizon; as the Renyi
parameter $n$ increases the temperature of the black hole decreases. If the CFT
possesses a sufficiently low dimension scalar operator the black hole will be
unstable to the development of hair. Thus, as $n$ is varied, the Renyi
entropies will exhibit a phase transition at a critical value of $n$. The
location of the phase transition, along with the spectrum of the reduced
density matrix $\rho$, depends on the dimension of the lowest dimension
non-trivial scalar operator in the theory.Comment: 21 pages, 7 figures, v3 - References added. Neumann boundary
  conditions added in section
Universal aspects of holographic Schwinger effect in general backgrounds

We consider universal aspects of a holographic Schwinger effect in general
backgrounds with an external homogeneous electric field. The argument is based
on the potential analysis developed in our previous work. Under some
conditions, there always exists a critical electric field, above which the
potential barrier vanishes and the system becomes unstable catastrophically.
The critical value agrees with the one obtained from the Dirac-Born-Infeld
action. For general confining backgrounds, we show that the Schwinger effect
does not occur when the electric field is weaker than the confining string
tension.Comment: 17 pages, v2:accepted versio
Coherence phenomena between initial and final state radiation in a dense
  QCD medium

In this work we investigate medium modifications to the interference pattern
between initial and final state radiation. We compute single gluon production
off a highly energetic parton that undergoes a hard scattering and subsequently
crosses a dense QCD medium of finite size. We extend our previous studies
obtained at first order in opacity by providing general results for multiple
soft scatterings and their specific formulation within the harmonic oscillator
approximation. We show that there is a gradual onset of decoherence between the
initial and final state radiation due to multiple scatterings, that opens the
phase space for large angle emissions. By examining the multiplicity of
produced gluons, we observe a potentially large double logarithmic enhancement
for dense media and small opening angles. This result points to a possible
modification of the evolution equations due to a QCD medium of finite size. We
briefly comment on the phenomenological consequences of this setup in
high-energy nuclear collisions.Comment: 33 pages, 2 figures. Fix typos and updated references. Discussion in
  the introduction updated. Accepted for publication in JHE
Equation of State of hot and dense QCD: Resummed perturbation theory
  confronts lattice data

We perform a detailed analysis of the predictions of resummed perturbation
theory for the pressure and the second-, fourth-, and sixth-order diagonal
quark number susceptibilities in a hot and dense quark-gluon plasma. First, we
present an exact one-loop calculation of the equation of state within
hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous
one-loop HTLpt calculation that employed an expansion in the ratios of thermal
masses and the temperature. We find that this expansion converges reasonably
fast. We then perform a resummation of the existing four-loop weak coupling
expression for the pressure, motivated by dimensional reduction. Finally, we
compare the exact one-loop HTLpt and resummed dimensional reduction results
with state-of-the-art lattice calculations and a recent mass-expanded
three-loop HTLpt calculation.Comment: 43 pages, 10 figures. v3: Matching published versio
F-Theory Compactifications with Multiple U(1)-Factors: Addendum

The purpose of this note is to extend the results obtained in
[arXiv:1303.6970] in two ways. First, the six-dimensional F-theory
compactifications with U(1) x U(1) gauge symmetry on elliptic Calabi-Yau
threefolds, constructed as a hypersurface in $dP_2$ fibered over the base
$B=\mathbb{P}^2$ [arXiv:1303.6970], are generalized to Calabi-Yau threefolds
elliptically fibered over an arbitrary two-dimensional base B. While the
representations of the matter hypermultiplets remain unchanged, their
multiplicities are calculated for an arbitrary B. Second, for a specific
non-generic subset of such Calabi-Yau threefolds we engineer SU(5) x U(1) x
U(1) gauge symmetry. We summarize the hypermultiplet matter representations,
which remain the same as for the choice of the base $B=\mathbb{P}^2$
[arXiv:1306.3987], and determine their multiplicities for an arbitrary B. We
also verify that the obtained spectra cancel anomalies both for U(1) x U(1) and
SU(5) x U(1) x U(1).Comment: 13pp, Addendum to arXiv:1303.697
Holographic Charged Renyi Entropies

We construct a new class of entanglement measures by extending the usual
definition of Renyi entropy to include a chemical potential. These charged
Renyi entropies measure the degree of entanglement in different charge sectors
of the theory and are given by Euclidean path integrals with the insertion of a
Wilson line encircling the entangling surface. We compute these entropies for a
spherical entangling surface in CFT's with holographic duals, where they are
related to entropies of charged black holes with hyperbolic horizons. We also
compute charged Renyi entropies in free field theories.Comment: 58 pages, v2 - figures fixed and references adde
New higher-derivative invariants in N=2 supergravity and the
  Gauss-Bonnet term

A new class of N=2 locally supersymmetric higher-derivative invariants is
constructed based on logarithms of conformal primary chiral superfields. They
characteristically involve a coupling to R_{\mu\nu}^2 - 1/3*R^2, which equals
the non-conformal part of the Gauss-Bonnet term. Upon combining one such
invariant with the known supersymmetric version of the square of the Weyl
tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The
construction is carried out in the context of both conformal superspace and the
superconformal multiplet calculus. The new class of supersymmetric invariants
resolves two open questions. The first concerns the proper identification of
the 4D supersymmetric invariants that arise from dimensional reduction of the
5D mixed gauge-gravitational Chern-Simons term. The second is why the pure
Gauss-Bonnet term without supersymmetric completion has reproduced the correct
result in calculations of the BPS black hole entropy in certain models.Comment: 45 pages; v2: version to appear in JHE