International Journal of Modern Physics: Conference Series

We discuss gluon scattering amplitudes/null-polygonal Wilson loops of super Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. We focus on the amplitudes/Wilson loops corresponding to the minimal surfaces in AdS₃, which are described by the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model. Using conformal perturbation theory and an interesting relation between the g-function (boundary entropy) and the T-function, we derive analytic expansions around the limit where the Wilson loops become regular-polygonal. We also compare our analytic results with those at two loops, to find that the rescaled remainder functions are close to each other for all multi-point amplitudes.

First, we give a brief review of recent development of lattice formulations for supersymmetric Yang-Mills (SYM) theories with extended supersymmetry, which preserves a part of supersymmetry on lattice. For cases of two dimensions, we can see that lattice models in such formulations lead to the target continuum theories with no fine-tuning. Namely, supersymmetries or some other symmetries not realized on the lattice are automatically restored in the continuum limit.

Next, we consider a mass deformation to and present its lattice formulation with keeping two supercharges. It provides a nonperturbative framework to investigate IIA matrix string theory. Moreover, since it has fuzzy sphere solutions around which four-dimensional theory is deconstructed, it will serve a nonperturbative formulation of four-dimensional which requires no fine-tuning. The rank of the gauge group is not restricted to large N. It opens a quite interesting possibility to test AdS/CFT correspondence in a stringy regime where string loop effects cannot be neglected. Also, for two-dimensional , a similar argument is possible to obtain four-dimensional on noncommutative space.

We consider an supersymmetric U(N) gauge theory with an adjoint chiral multiplet. By developing a self-consistent Hartree-Fock approximation to the leading order which is reminiscent of that of the BCS/NJL in the superconductivity/chiral symmetry, we show that the supersymmetry is spontaneously broken, giving a mixed Majorana-Dirac mass term for gaugino due to the nonvanishing D-term VEV and F-term one induced by D-term.

We study the Kähler potential of charged matter fields, whose profiles have a peak on their matter curve — on an "intersection" of 7-branes, in an F-theory compactification. It is shown that the Kähler potential is exactly given by the integral over the matter curve, but not by the integral over the whole GUT surface of 7-branes. This talk is based on our paper "A Note on Kahler Potential of Charged Matter in F-theory," in collaboration with Yoichi Tsuchiya and Taizan Watari.

I will discuss how an unexpected form of trace anomaly can be obtained from holographic models with no simple string interpretation. In addition to the usual trace anomaly, Euler density and Weyl tensor squared, we pursue the possibility that it is given by Ricci scalar and Hirzebruch-Pontryagin density. It has a deep connection with scale but non-conformal field theories and their holographic dual. I would like to urge you to judge whether such holographic theories are consistent or pathological.

Besides ordinary branes such as D-branes, string theory is known to contain exotic branes which are related to ordinary branes by U-duality. Exotic branes are codimension-two objects and have non-trivial U-duality monodromies around them. This means that they are intrinsically non-geometric. Even if one starts with a system only with ordinary branes, exotic branes can be spontaneously generated by the supertube effect. We argue that, if one puts together more than two mutually supersymmetric branes, then, by a multi-stage supertube effect, the system will polarize into an exotic brane extending along an arbitrary surface, dubbed as the superstratum. We conjecture that, black holes in string theory, which are constructed by combining multiple ordinary branes, necessarily include exotic superstrata as their microscopic ingredients. We review the argument for the existence of superstrata and the recent progress toward constructing examples of superstrata in the framework of supergravity in six dimensions.

The β-deformed matrix models of Selberg type are introduced. They are exactly calculable by using the Macdonald-Kadell formula. With an appropriate choice of the integration contours and interactions, the partition function of the matrix model can be identified with the Nekrasov partition function for SU(2) gauge theory with N_f = 4. Known properties of good q-expansion basis for the matrix model are summarized.

We discuss the gravity duals of SO/USp superconformal quiver gauge theories on M5-branes which are localized on top of ℝ⁵/ℤ₂ and wrapping on a Riemann surface of genus g. We concentrate on Riemann surfaces with no punctures and show that the gravity solutions are classified by the genus g of the Riemann surface and the torsion part of the four-form flux.

We find that, apart from the instanton contributions, the all genus partition function of the ABJM matrix model sums up to the Airy function. We present the result, discuss its implication and also summarize some further progress.

We find a Nekrasov-type expression for the Seiberg–Witten prepotential for the six-dimensional non-critical E₈ string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E₈ strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.

We study the chiral condensate in dense baryonic medium by the use of the generalized Sakai-Sugimoto model of holographic QCD. The chiral condensate is identified with the vacuum expectation value of the open Wilson line operator. We evaluate it by the minimal area of open string world-sheet whose boundary is the V-shape flavor D8-branes. As a result, we find that the chiral condensate decreases in low baryon density and increases in high density. This decreasing behavior is in agreement with the expectation from QCD.

Killing–Yano symmetry has played an important role in the study of black hole physics. In supergravity theories, Killing–Yano symmetry is deformed by the presence of the fluxes which can be identified with skew-symmetric torsion. Therefore, we attempt to classify spacetimes admitting Killing-Yano symmetry with torsion. In particular, the classification problem of metrics admitting a principal Killing–Yano tensor with torsion is discussed.

We explore a duality between five-dimensional supersymmetric linear quiver gauge theories compactified on a circle, which are the five-dimensional uplifts of four-dimensional superconformal linear quiver theories. We find a correspondence between the gauge theory parameters of two dual theories, under which identical infrared effective coupling constants are obtained on the Coulomb branch. Two independent approaches using M-theory and the topological string theory give a consistent result.

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to algebra as one of the promising direction towards the proof of the remaining part.

A direct application of the lattice Monte Carlo method to QCD with a finite baryon chemical potential is difficult due to the sign problem. We introduce a novel approach to avoid the sign problem, which is inspired by the string theory.

In this note, we study the dipole coupling effect of holographic fermion in a charged dilatonic black hole proposed by Gubser and Rocha.¹ It is found that the property of Fermi liquid is rigid under perturbation of dipole coupling, and the Fermi momentum is linearly shifted. A gap is dynamically generated as the coupling becomes large enough and the Fermi surface ceases to exist as the bulk dipole coupling further increases.

Non-critical string/M theory is a solvable model which has been studied to reveal various non-perturbative aspects of string theory with providing new key concepts to the next developments of string theory. Here we show some recent progress in study of Stokes phenomenon in non-critical string theory of the multi-cut two-matrix models. In particular, we argue that it is Stokes phenomenon which allows us to know concepts of non-perturbative completion with analytic study of string-theory landscape from the first principle.

We report on our recent studies on holographic Wilsonian renormalization group in a general class of asymptotically AdS backgrounds with a Maxwell gauge field.

We study the large-N renormalization group of scalar field theory on a fuzzy sphere. We carry out perturbative analysis and formulate the renormalization group equation. We then search for fixed points and investigate their properties.

It is known that infinitely many linear relations among string scattering amplitudes appear in high energy limit. These linear relations would imply a symmetry structure that is not manifest before taking the high energy limit. Motivated by this observation, we study an effective field theory of massive spin-2 and spin-1 particles, and try to understand what kind of structure reproduces the linear relations among the amplitudes of bosonic open string.

We find novel phase transitions and critical phenomena that occur only outside the linear-response regime of current-driven nonequilibrium states, by using the AdS/CFT correspondence. We compute the nonlinear non-ballistic quark-charge conductivity of a strongly-interacting (3 + 1)-dimensional gauge theory, and we find that the system exhibits a nonequilibrium first-order and second-order phase transitions where the sign of the differential conductivity flips at finite current density. The present work provides a new example of nonequilibrium phase transitions and nonequilibrium critical points.

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Q_l in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Q_l, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

We consider two supersymmetric gauge theories connected by an interface and the gravity dual of this system. This interface is expressed by a fuzzy funnel solution of Nahmfs equation in the gauge theory side. The gravity dual is a probe D5-brane in AdS₅ × S⁵. The potential energy between this interface and a test particle is calculated in both the gauge theory side and the gravity side by the expectation value of a Wilson loop. In the gauge theory it is evaluated by just substituting the classical solution to the Wilson loop. On the other hand it is done by the on-shell action of the fundamental string stretched between the AdS boundary and the D5-brane in the gravity. We show the gauge theory result and the gravity one agree with each other.

On the de Sitter background, the gravitational propagator contains an infra-red logarithm term which breaks the de Sitter symmetry. We investigate how such soft gravitons affect the local dynamics of matter fields. We show that the infra-red logarithms do not spoil Lorentz invariance in scalar, Dirac and gauge field theories. In the interacting field theory with quartic, Yukawa and gauge interactions, we find that the effective couplings are time dependent and the evolutions are physical as their relative scaling exponents are gauge invariant.

Gravity, itself a gauge theory of a spin 2 field, can be extended to a higher spin gauge theory on AdS spaces. Recently, Gaberdiel and Gopakumar conjectured that a large N limit of a 2d minimal model is dual to a bosonic subsector of a higher spin supergravity theory on 3d AdS space. We propose and test the untruncated supersymmetric version of this conjecture where the dual CFT is a large N limit of the CP^N Kazama-Suzuki model.

The excited state spectrum of AdS₅ × S⁵ string can be computed exactly by the mirror TBA equations. We discuss an equivalent, smaller set of equations called hybrid nonlinear integral equations (NLIE). The hybrid NLIE is written by new dynamical degrees of freedom, analogous to spinon variables in condensed matter systems. This derivation is applicable to any integrable systems which obey A₁ T-system equipped with certain analyticity conditions. A case study of orbifold Konishi state shows that the new method relieves the problem of criticality in the mirror TBA equations.

We study a self-consistent solution of the semi-classical Einstein equation including the back reaction from the Hawking radiation. Our geometry is constructed by connecting flat space and the outgoing Vaidya metric at the locus of the shock wave. In order to prove that this is the self-consistent solution, we first show that the Weyl anomaly is canceled if we take the effects of the fluctuations of the metric into account. We further demonstrate that the Hawking radiation occurs even if the geometry has no horizon. Then, the energy-momentum tensor is found to be consistent with the semi-classical Einstein equation. Since our geometry has neither horizon nor singularity, all matters inside the black hole finally come back to infinity. Therefore, no information is lost by the black hole evaporation. Furthermore, we take into account the gray-body factor. We construct a stationary solution for a black hole in the heat bath and estimate the entropy. The entropy-area law is reproduced by the volume integration of the entropy density over the inside of the horizon, and the black hole can be treated as an ordinary thermodynamic object.

After constructing the -brane background, which is a T-fold in string theory, from a D7-brane via U-duality, we derived the fundamental string solution rotating around it. Reflecting that the background is not axisymmetric, the string solution also changes its shape during its rotation. However, we found that the background is indeed axisymmetric in the sense of doubled geometry, by explicitly finding a generalized Killing vector. Moreover, the string charge density vector is found to be generalized Lie transported along the generalized Killing vector.

We argue a squashing deformation of 3D supersymmetric theories on round S³, which preserves SU(2)_L × U(1)_r isometry and the supersymmetries. We stress that the choice of a supersymmetry for the localization affects whether the partition function calculated using the supersymmetry depends on the squashing parameter or not.

We develop a general method based on the integrability for computing the holographic three point functions for the large spin limit of Gubser-Klebanov-Polyakov (GKP) strings, which correspond to twist-2 operators in super Yang-Mills.

We study reduced matrix models obtained by the dimensional reduction of quiver Chern-Simons theories on S³ and show that, around a certain multiple fuzzy sphere background, the reduced models are equivalent to the original theories in the large-N limit. This is regarded as a large-N reduction on S³. By using the localization technique, we prove the large-N equivalence with respect to supersymmetric observables.

We derive a general formula for an index for superconformal field theories. In the computation, 1-loop and monopole bubbling effects are taken into account. Our computation is compatible with S-dualities in the theories and the holographic principle which maps Wilson line operators in the SYMs to macroscopic objects in AdS₅ × S⁵.

We show Yangian and quantum affine symmetries are realized in two-dimensional non-linear sigma models with squashed spheres target spaces. According to these symmetries, there are two descriptions for the classical dynamics. In each description, a Lax pair and the corresponding monodromy matrix are constructed. Both Lax pairs reproduce the same equations of motion and hence they are equivalent. We show the gauge-equivalence by constructing a map between monodromy matrices with the relation of spectral parameters.

We calculate a superconformal index of the half-BPS duality domain wall inserted at the great S² of S³ in SU(2) super Yang-Mills theory on S¹ × S³.

The Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction for noncommutative U(N) instantons is revisited. The origin of the instanton number is elucidated, including the case of the U(1) instantons. The group actions on the instantons are argued.

We reconsider the realization of baryons in the Sakai-Sugimoto model. It has previously been shown that, at least with the standard approach to calculations of baryon properties in the theory, one does not reproduce some model-independent predictions for the behavior of baryon electromagnetic form factors connected with long-range pion physics. It is suspected that the pion contributions has been dropped because of the linearization approximations. We study the long-range properties of baryons without relying on the approximations. The baryon solution we obtain gives the correct result for the model-independent ratio of the form factors.

We explain the relativistic theory of viscoelasticity which we have recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. This theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We then present conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We particularly show that a conformal second-order fluid with all possible parameters in the constitutive equations can be obtained without breaking the hypothesis of local thermodynamic equilibrium, if the conformal fluid is defined as the long time limit of a conformal second-order viscoelastic system.

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E₈ × E₈ heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

We study the 1/2 BPS condition of Wilson loop on squashed three-sphere, and find that the solution becomes torus knot or unknot. We also calculate the expectation value of 1/2 BPS Wilson loops by using localization technique with the gauge group U(2) and Wilson loop as fundamental representation. And it completely matches with known results.

Recent Monte Carlo study on the Lorentzian matrix model for superstring theory revealed that an expanding (3 + 1)d universe appears dynamically from (9 + 1)d. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the three expanding spaces. As a complementary approach to possible future beyond the numerical result, we discuss classical solutions for the Lorentzian matrix model and their properties.

We have established a relation between the four-dimensional chiral index in F-theory compactifications and the three-dimensional Chern-Simons coupling in M-theory compactifications by using F-theory - M-theory duality. The content of this article is based on our recent paper,¹ which is in collaboration with Thomas W. Grimm.

We show that the ABJM theory, which is an superconformal U(N) × U(N) Chern-Simons matter theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model derived by using the localization method. Here we calculate the free energy, and show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion.