International Journal of Modern Physics A

We analyze the coupled supergravity and Yang-Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gM_pl where g is the gauge coupling constant and M_pl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently.

We review our recent formulation^1,2 of computing entanglement entropy in a holographic way. The basic examples can be found by applying AdS/CFT correspondence and the holographic formula has successfully been checked in many examples of conformal field theories. We also explain the covariant formulation of holographic entanglement entropy which is closely related to the covariant entropy bound (Bousso bound) in an interesting way.

The universal behavior of Hawking radiation is originated in the conformal symmetries of matter fields near the black hole horizon. We explain the origin of this universality based on (1) the gravitational anomaly and its higher-spin generalizations and (2) conformal transformation properties of fluxes.

Recently Maldacena conjectured that the long folded open string in noncritical string theory is described by the non-singlet sectors of matrix quantum mechanics. In this paper, we first describe how to obtain the exact wave functions of this system when the sign of the potential is reverted, based on a work with Y. Hatsuda. The wave functions are labeled by three Young diagrams and the degeneracy associated with it is given by the group theoretical quantities. In the second part, based on a work with J.-E. Bourgine, K. Hosomichi and I. Kostov, we derive the scattering amplitude of two long strings and which coincides with the result from the Liouville theory. It generalizes the result of the one-body scattering by Kostov and uses the relation with the two-matrix model correlation functions.

We investigate 3D Yang-Mills theory coupled to an adjoint scalar, which can be regarded as a zeroth order approximation in (de)constructing 4D Yang-Mills theory. We develop a new algorithm to obtain the renormalized Hamiltonian with the Karabali-Nair variable, by carefully identifying finite local counterterms. We also discuss how this formalism can be applied to obtain glueball spectrum.

We review the Pohlmeyer reduction of the superstring sigma model on AdS_n × Sⁿ leading to a gauged WZW model with an integrable potential. In particular, we consider the case of GS superstrings on AdS₃ × S³ supported by RR flux. The bosonic part of the reduced Lagrangian is given by the sum of the complex sine-Gordon Lagrangian and its sinh-Gordon counterpart. We determine the corresponding fermionic part and discuss possible 2d supersymmetry of the reduced action.

A short summary of approximate approach to the study of minimal surfaces in AdS, based on solving Nambu-Goto equations iteratively. Today, after partial denunciation of the BDS conjecture, this looks like the only constructive approach to understanding the ways of its possible modification and thus to saving the Alday-Maldacena duality. Numerous open technical problems are explicitly formulated throughout the text.

We review recent developments in calculation of the gluon scattering amplitudes in super Yang-Mills theory at strong coupling via AdS/CFT correspondence. We discuss certain class of 6 and 8 point amplitudes at strong coupling, which can be obtained by cutting and gluing the 4-point amplitude.

Recent progress towards understanding a strong coupling expansion for various superconformal field theories in four dimensions is described. First, the case of the maximally supersymmetric Yang Mills theory is analyzed, as well as many calculations that can be done directly at strong coupling and matched to the AdS dual geometry. Also, this understanding is extended to other AdS duals where the sphere is replaced by a Sasaki-Einstein manifold. Particular emphasis is made on matching exactly part of the supergravity dual spectrum of various of these field theories by using wave function methods.

We consider the purely gravitational fourth-order (in the spacetime curvature) quantum corrections to the Einstein-Hilbert gravity action, coming from superstrings in the leading order with respect to the Regge slope parameter, and study their impact on the evolution of the Hubble scale in the context of the FRW cosmology, in four spacetime dimensions. We propose the generalized Friedmann equations, and rule out the most naive (Bel-Robinson tensor squared) gravity. Our new cosmological equations have exact inflationary solutions without a spacetime singularity.

We perform a direct test of the gauge/gravity duality by studying one-dimensional U(N) gauge theory with 16 supercharges at finite temperature using Monte Carlo simulation. In the 't Hooft large-N limit and in the strong coupling limit, the model is expected to have a dual gravity description in terms of the near-extremal black 0-brane solution in ten-dimensional type IIA supergravity. Our results provide the first example, in which the microscopic origin of the black hole thermodynamics is accounted for by solving explicitly the strongly coupled dynamics of the open strings attached to the D-branes.

We extend the large N reduction and the compactification in matrix models to those on manifolds represented as fiber bundles. We also discuss application of our results to the AdS/CFT correspondence and topological field theories.

This paper gives a brief review of recent results on higher dimensional black hole solutions. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lü-Pope is the only spacetime admitting a rank-2 conformal Killing-Yano tensor with a certain symmetry.

We review the matter induced part of the effective superpotential of , U(N) gauge model in which supersymmetry is spontaneously broken to . We derive this by the diagrammatical computation and by using the properties of the chiral ring and the generalized Konishi anomaly equations.

We investigate a possibility for a black hole to be created during closed string tachyon condensation. For the case of a bulk closed string tachyon, we find classical solutions of a low energy effective theory which has a black hole in the space-time. On the other hand, for the case of a localized closed string tachyon, a black hole, if created, would be of the string size and it would quickly evaporate.

We analyze the attractor mechanism for the D0-D4 black hole solution in the four-dimensional supergravity. Our analyses are based on new exact solutions, which show explicitly the attractor mechanism for the extremal non-BPS black holes. Our solutions take into account the moduli as general complex fields, while in almost all the non-BPS solutions obtained by previous authors, the moduli fields are restricted to be purely imaginary.

We address issues on the origin of gravity and the dark energy (or the cosmological constant) from the perspectives of emergent gravity. We discuss how the emergent gravity reveals a noble, radically different picture about the origin of spacetime, which is crucial for a tenable solution of the cosmological constant problem. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity.

We construct spacetime supersymmetric, modular invariant partition functions for type II and heterotic strings on the conifold-type singularities such that they include contributions coming from the discrete-series representations of SL(2, R). In particular for the E₈ × E₈ heterotic case, they are in the 27 representation of E₆ and localized on a four-dimensional "brane" at the tip of the cigar geometry.

We briefly report on some recent progresses in the computation of B-brane superpotentials for Type II strings compactified on Calabi–Yau manifolds, obtained by using a paramatrization of tubular neighborhoods of complex submanifolds, also known as local spaces. In particular, we propose a closed expression for the superpotential of a brane on a genus-g curve in a Calabi–Yau threefold for the cases in which there exists a holomorphic projection from the local space around the curve to the curve itself.

We present a stringy realization of the ISS metastable SUSY breaking model with moduli stabilization. The mass moduli of the ISS model is stabilized by gauging of a U(1) symmetry and its D-term potential. The SUSY is broken both by F-terms and D-terms. It is possible to obtain de-Sitter vacua with a vanishingly small cosmological constant by an appropriate fine-tuning of flux parameters. The content of this article is based on our recent paper¹, which is in collaboration with Yu Nakayama (Berkeley) and Tsutomu Yanagida (Tokyo).

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity.

We investigate the M5-brane description of the Wilson surface operators in six-dimensional (2,0) superconformal field theory from AdS/CFT correspondence. We consider the Wilson surface operators in high-dimensional representation, whose description could be M5-brane string soliton solutions in AdS₇ × S⁴ background. We construct such string soliton solutions from the covariant M5-brane equations of motion and discuss their properties. The supersymmetry analysis shows that these solutions are half-BPS. Furthermore, we discuss the operator product expansion of the Wilson surface operators in higher dimensional representation using their corresponding M5-brane configurations.

We address the question of determining the prepotential of the gauged supergravity resulting from a compactification of M-theory on AdS₄ × Y₇. We make a concrete proposal for the prepotential in the case of toric Sasaki-Einstein Y₇. Comparison with direct Kaluza-Klein computations show that the proposal is correct in certain cases, but requires modification in general.

We revealed a relationship between the plane wave matrix model (PWMM) and N=4 super Yang-Mills (SYM) theory on R × S³: N=4 SYM on R × S³ is equivalent to the theory around a certain vacuum of PWMM. It is suggested from this relation that N=4 SYM on R × S³ is regularized by PWMM in the planar limit. Because PWMM originally possesses the gauge symmetry and SU(2|4) symmetry, this regularization also preserves these symmetries. In order to check the validity of this matrix regularization method, we calculate the Ward identity and the beta function at the 1-loop level. We find that the Ward identity is satisfied and the beta function vanishes in the continuum limit. The former result is consistent with the gauge symmetry of PWMM. The latter suggests the possibility that the conformal symmety is restored in the continuum limit.

We describe toy models of cosmology in asymptotically AdS space-times which have natural gauge theory duals. For spacetimes containing null singularities we argue that the gauge theory provides a well defined evolution in light front time even though the gravity description does not. For models with spacelike singularities examined so far, we identify the signature of such singularities in the gauge theory. However, it is not clear whether these singularities can be "resolved".

We briefly review the construction of multi-centered black hole solutions in type IIA string theory. We then discuss a decoupling limit which embeds these solutions in M-theory on AdS₃ × S² × CY, and discuss some aspects of their dual CFT interpretation. Finally, we consider the quantization of these solutions and applications to the wall-crossing formula and the "fuzzball" proposal.

We construct solitonic states in the OSp invariant string field theory, which are BRST invariant in the leading order of regularization parameter. One can show that these solitonic states describe D-branes and ghost D-branes, by calculating the scattering amplitudes.

We holographically derive entropy of (near) extremal black holes as entanglement entropy of conformal quantum mechanics(CQM) living in two boundaries of AdS₂.

We completely accomplish the canonically covariant quantization of RNS superstrings in the pp-wave background with torsion which is equivalent to the NS-NS flux. In this quantization, we construct general operator solutions which satisfy all the equations of motion and all the canonical (anti)commutation relations. Because the general operator solutions can be composed of only free modes, we also call them free-mode representations. Using the covariant free-mode representations, we calculate the anomaly in the super-Virasoro algebra and determine the number of dimensions of spacetime and ordering constant from the nilpotency condition of the BRST charge in the NS-NS pp-wave.

Domain walls in gauge theory with non-Abelian flavor symmetry possess normalizable Nambu-Goldstone zero modes associated with spontaneously broken non-Abelian flavor symmetry. We construct the moduli space metric as the effective field theory of walls. The Nambu-Goldstone modes spread between two domain walls and their rotation induces long-range repulsive force. We also construct a bound state of domain walls. This article is based on the work with M. Eto, M. Nitta, K. Ohashi and N. Sakai¹.

We discuss extension of soliton theory and integrable systems to non-commutative (NC) spaces, focusing on integrable aspects of NC Anti-Self-Dual Yang-Mills (ASDYM) equations. We give exact soliton solutions (with both finite- and infinite-action solutions) by means of Bäcklund transformations. In the construction of NC soliton solutions, one kind of NC determinants, quasideterminants, play crucial roles. This is partially based on collaboration with C. R. Gilson and J. J. C. Nimmo (Glasgow).

We compute finite-size corrections to dyonic giant magnons in two ways¹. One is by using classical string solutions corresponding to finite-size dyonic giant magnons called "helical strings". The other is by applying the Lüscher formula known in relativistic quantum field theory to the case in which incoming particles are boundstates. We find these two methods lead the same result.

We find a new family of classical oscillating strings with large winding numbers, which are constructed by interchanging τ and σ of helical strings' solutions. We also give a finite-gap interpretation of interchanging τ and σ. Gauge dual operators are discussed at the end.

Atick and Witten have proposed the Hagedorn transition of closed strings via condensation of 'winding tachyon'. But we have not known the stable minimum of this tachyon potential yet. On the other hand, we have previously shown that a phase transition occurs near the Hagedorn temperature and D9-brane– -brane pairs become stable. We present a conjecture that D9-brane– -brane pairs are created by the Hagedorn transition of closed strings. We will show some circumstantial evidences for this conjecture.

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.

We study boundary states in (p,q) minimal superstring theory, combining the explicit form of matter wave functions. Within the modular bootstrap framework, Cardy states of (p, q) minimal superconformal field theory are completely determined in both cases of the different supercharge combinations, and the remaining consistency checks in the super-Liouville case are also performed. Using these boundary states, we determine the explicit form of FZZT- and ZZ-brane boundary states both in each GSO projection. Annulus amplitudes of FZZT branes are evaluated and principal FZZT branes are identified. In particular, we found that these principal FZZT branes do not satisfy Cardy's consistency conditions for each other and play a role of order/disorder parameters of a Kramers-Wannier duality in spacetime of this superstring theory. This presentation is based on the paper¹.

N = 2 supersymmetric Yang-Mills theory with flavor hypermultiplets at finite temperature is studied for finite quark number density (n_b) by a dual supergravity background with nontrivial dilaton and axion. The quarks and their number density n_b are introduced by embeddings a probe D7 brane. We find a critical value of the chemical potential at the limit of n_b = 0, and it coincides with the effective quark mass for n_b = 0. At this point, a transition of the D7 embedding configurations occurs between their two typical ones. The phase diagrams of this transition are shown in the plane of chemical potential versus temperature for Yang-Mills theory at finite temperature. In this phase transition, the order parameter is considered as n_b. This result seems to be reasonable since this theory is in the quark deconfiment phase.

We report on the boundary state of superstring in the open string channel, which describes the superconformal field theory of open string emission and absorption by D-brane.

We study the four dimensional gauge theory within Wilsonian Renormalization Group (WRG) method. The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda. We elucidated the relation of our Wilson master action with that derived by Ref. 2 and, in particular, showed that our BV Master equation really reproduced the Sonoda's WT identity for the Wilson action in QED. (This is a proceeding to the conference based on the poster given by E.I.).

In this poster, we study the boundary states of the three-state Potts model coupled to two dimensional gravity, which we call Z₃ extended minimal string. We find that two different boundary states of this model can be identified with a shift of the boundary cosmological constant. We also point out that the boundary states are classified with respect to the symmetry of the theory. This presentation is based on Ref. 1 to appear soon.

We investigate the Atiyah-Singer index theorems with torsion given by Neveu-Schwarz three-form flux H under the condition dH = 0 in flux compactification scenarios with non-trivial background fields in string theories. Using an identification between the Clifford algebra on the geometry and the canonical quantization condition in quantum mechanics, we explicitly reformulate the Dirac index on manifolds with torsion, which will provides a fundamental information to effective theories derived from string theory. In the same analogy we also reformulate the Euler characteristics and the Hirzebruch signatures in the framework of quantum mechanics.

We find a new quantum Yangian symmetry of AdS/CFT S-matrix, which does not have the original Lie algebra 𝔰𝔲(2|2) analogue, and persue the origin of this symmetry in exceptional superalgebra 𝔡(2, 1; ε) , which recovers 𝔰𝔲(2|2) when the paramater ε taken to zero.

We study a finite temperature string in curved space, especially in AdS₃ and BTZ black hole background. We extract Hagedorn behavior of strings and argue thermodynamic properties in thermal AdS₃ as well as in BTZ black hole background. In particular, we find the Hagedorn temperature of string on AdS₃, which depends on the AdS₃ curvature scale. We also find a tachyonic divergence for a BTZ black hole of string scale.

We briefly review a tunneling picture of rotating D3-brane solutions. By applying the "double Wick rotation" to the Lorentzian solutions, we construct Euclidean solutions. The solutions are composed of dual giant gravitons and spike D3-brane solutions, and their classical actions reproduce expectation values of the k-th symmetric Wilson loops as well as correlation functions of dual giant graviton operators as expected.

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli space approximation. This talk is based on works in collaboration with M.Eto, T.Fujimori, M.Nitta, K.Ohashi, and N.Sakai^1,2.

We consider black p-branes on square torus. We find an indication of a cascade of Gregory-Laflamme transitions between black p-brane and (p - 1)-brane. Through AdS/CFT correspondence, these transitions are related to the breakdown of the U(1) symmetry in super Yang-Mills on square torus. We argue a relationship between the cascade and recent Monte-Carlo data. This talk is based on Ref. 1.

We briefly review a holography of non-relativistic (NR) string on AdS₅×S⁵. The NR string can be regarded as a semiclassical string around an AdS₂ classical solution corresponding to a straight Wilson line in the gauge-theory side. Exciting non-normalizable modes of the NR string gives source term insertions on the Wilson line. For normalizable modes we discuss a relation to a conformal quantum mechanics.

Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar braided noncommutative field theory in Lie-algebraic noncommutative spacetime, which has a Hopf algebraic translational symmetry. We construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter. We then find the massless moduli field which propagates on the domain wall soliton. This work is based on arXiv:0711.3059.

It has not been clarified whether a matrix model can describe various vacua of string theory. In this talk, we show that the IIB matrix model includes type IIA string theory¹. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

We reformulate bosonic boundary string field theory in terms of boundary state. In our formulation, we can formally perform the integration of target space equations of motion for arbitrary field configurations without assuming decoupling of matter and ghost. This is a short summary of our contribution to the international workshop "Progress of String Theory and Quantum Field Theory" at Osaka City University (December 7-10, 2007).

It is well known that higher-dimensional black objects with translational invariance are unstable, which is called Gregory-Laflamme instability. There is a question if this instability is eliminated by adding a scalar hair to the black objects. For the first step, we investigate a regular topological string solution and its stability in the five-dimensional Einstein-Higgs system. Linear analysis shows that the string solution is stable against non-uniform perturbations.

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup of SU(2). The string theory analysis predicts that the number and the order of the fixed points of this discrete subgroup acting on S2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by utilizing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks.

Even though the chaotic inflation is one of the most popular inflation models for its simple dynamics and compelling resolutions to the initial condition problems, its realization in supergravity has been considered a challenging task. We discuss how the chaotic inflation dominated by the D-term can be induced in supergravity, which would give a new perspective on the inflation model building in supergravity.

In this contribution we describe some soliton based techniques for generating classical AdS string solutions. The methods introduced are useful for further understanding of rotating AdS configurations with spikes which correspond to higher twist operators in SYM theory. The main identification (accomplished in arXiv:0712.1193) between solitons and string spikes is reviewed and extended. We desribe how inverse scattering technique can be applied for reconstructing AdS string configurations from soliton solutions of sinh-Gordon theory (in the example of AdS₃).

The relation between brane charge conservation law in fivebrane system described by orientifolded brane tilings and the gauge anomaly cancellation in the corresponding gauge theories is summarized.

We give a brief account of the recent progresses in super Yang-Mills theories based in particular on the application of Nekrasov's instanton technology to the case of supersymmetry. We have developed a first-principle formalism from which any chiral observable in the theory can be computed, including in strongly coupled confining vacua. The correlators are first expressed in terms of some external variables as sums over colored partitions. The external variables are then fixed to their physical values by extremizing the microscopic quantum superpotential. Remarquably, the results can be shown to coincide with the Dijkgraaf-Vafa matrix model approach, which uses a totally different mathematical framework. These results clarify many important properties of theories, related in particular to generalized Konishi anomaly equations and to Veneziano-Yankielowicz terms in the glueball superpotentials. The proof of the equivalence between the formalisms based on colored partitions and on matrices is also a proof of the open/closed string duality in the chiral sector of the theories.

We argue that the Nekrasov's partition function with two equivariant parameters is reproduced by the method of topological vertex, if we introduce a refined version of the vertex. Our refined topological vertex is expressed in terms the specialization of the Macdonald functions which is related to the equivariant character of the Hilbert scheme of ℂ². We provide diagrammatic rules for computing the partition function.

We study loop operators of 5d SYM in Ω background. Computation of their correlation functions is described. For the case of U(1) theory, the generating function reproduces the partition function of melting crystal model with external potential. We argue the common integrable structure of 5d SYM in Ω background and melting crystal model. An extension of the Seiberg-Witten geometry of the U(1) theory is presented.

I discuss my recent attempt in search of a new framework for quantum field theory of D branes. After explaining some motivations in the background of this project, I present, as a first step towards our goal, a second-quantized reformulation of the U(N) Yang-Mills quantum mechanics in which the D0-brane creation-and-annihilation fields connecting theories with different N are introduced. Physical observables are expressed in terms of bilinear forms of the D0 fields. The large N limit is briefly treated using this new formalism.