We show that Nekrasov instanton partition function for SU(N) gauge theories
satisfies recursion relations in the form of U(1)+Virasoro constraints when
{\beta} = 1. The constraints give a direct support for AGT conjecture for
general quiver gauge ...

We study the inner product of Bethe states in the inhomogeneous periodic XXX
spin-1/2 chain of length L, which is given by the Slavnov determinant formula.
We show that the inner product of an on-shell M-magnon state with a generic
M-magnon state ...

We study the inner product of Bethe states in the inhomogeneous periodic XXX
spin-1/2 chain of length L, which is given by the Slavnov determinant formula.
We show that the inner product of an on-shell M-magnon state with a generic
M-magnon state ...

Motivated by application to multiple M5 branes, we study some properties of
non-Abelian two-form gauge theories. We note that the fake curvature condition
which is commonly used in the literature would restrict the dynamics to be
either a free the...

An intriguing coincidence between the partition function of super Yang-Mills
theory and correlation functions of 2d Toda system has been heavily studied
recently. While the partition function of gauge theory was explored by
Nekrasov, the correlati...

We give some evidences which imply that W(1+infinity) algebra describes the
symmetry behind AGT(-W) conjecture: a correspondence between the partition
function of N=2 supersymmetric quiver gauge theories and the correlators of
Liouville (Toda) fie...

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge
fields) in 6 dimensions with a spatial direction compactified on a circle of
radius R. It has the following two properties. (1) It reduces to the Yang-Mills
theory in 5 dim...

We give some evidences of the AGT-W relation between SU(3) quiver gauge
theories and A_2 Toda theory. In particular, we derive the explicit form of
5-point correlation functions in the lower orders and confirm the agreement
with Nekrasov's partiti...

We give some evidences of the AGT-W relation between SU(3) quiver gauge
theories and A_2 Toda theory. In particular, we derive the explicit form of
5-point correlation functions in the lower orders and confirm the agreement
with Nekrasov's partiti...

We discuss the correspondence between degenerate fields of the W_N algebra
and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2
superconformal gauge theories. Namely, we find that the type of degenerate
fields of the W_N algeb...

In our previous paper, it was shown that BLG model based on a Lorentzian
metric 3-algebra gives Dp-brane action whose worldvolume is compactified on
torus T^d (d=p-2). Here the 3-algebra was a generalized one with d+1 pairs of
Lorentzian metric ge...

We construct a class of Lie 3-algebras with an arbitrary number of pairs of
generators with Lorentzian signature metric. Some examples are given and
corresponding BLG models are studied. We show that such a system in general
describes a supersymme...

We construct a class of Lie 3-algebras with an arbitrary number of pairs of
generators with Lorentzian signature metric. Some examples are given and
corresponding BLG models are studied. We show that such a system in general
describes a supersymme...

We show that there exists a cut-off version of Nambu-Poisson bracket which
defines a finite dimensional Lie 3-algebra. The algebra still satisfies the
fundamental identity and thus produces N=8 supersymmetric BLG type equation of
motion for multip...

We investigate the Bagger-Lambert-Gustavsson model associated with the
Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that
the model is a gauge theory associated with the volume-preserving
diffeomorphism in the three-dime...

We present two derivations of the multiple D2 action from the multiple
M2-brane model proposed by Bagger-Lambert and Gustavsson. The first one is to
start from Lie 3-algebra associated with given (arbitrary) Lie algebra. The Lie
3-algebra metric i...

Recently an action based on Lie 3-algebras was proposed to describe
M2-branes. We study the case of infinite dimensional Lie 3-algebras based on
the Nambu-Poisson structure of three dimensional manifolds. We show that the
model contains self-dual ...

Motivated by the recent proposal of an N=8 supersymmetric action for multiple
M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the
fundamental identity and the relation with Nambu-Poisson bracket. Some new
algebras not k...

We derive boundary state of superstring in the open string channel. It
describes the superconformal field theory of open string emission and
absorption by D-brane. We define the boundary state by conformal mappings from
upper half plane with opera...

Based on an explicit computation of the scattering amplitude of four open
membranes in a constant 3-form background, we construct a toy model of the
field theory for open membranes in the large C field limit. It is a
generalization of the noncommu...

We study the non-singlet sectors of matrix quantum mechanics (MQM) through an
operator algebra which generates the spectrum. The algebra is a nonlinear
extension of the W_\infty algebra where the nonlinearity comes from the angular
part of the mat...

We study the non-singlet sectors of matrix quantum mechanics (MQM) through an
operator algebra which generates the spectrum. The algebra is a nonlinear
extension of the W_\infty algebra where the nonlinearity comes from the angular
part of the mat...

We generalize the idea of boundary states to the open string channel. They
describe emission and absorption of open strings in the presence of
intersecting D-branes. We construct the explicit oscillator representation for
the free boson and fermio...

We generalize the idea of boundary states to open string channel. They
describe the emission and absorption of the open string in the presence of
intersecting D-branes. We study the algebra between such states under the star
products of string fie...

We generalize the idea of boundary states to open string channel. They
describe the emission and absorption of the open string in the presence of
intersecting D-branes. We study the algebra between such states under the star
products of string fie...

We show that boundary states in the generic on-shell background satisfy a
universal nonlinear equation of closed string field theory. It generalizes our
previous claim for the flat background. The origin of the equation is
factorization relation o...

We show that boundary states in the generic on-shell background satisfy a
universal nonlinear equation of closed string field theory. It generalizes our
previous claim for the flat background. The origin of the equation is
factorization relation o...

With some assumptions, the algebra between Ishibashi states in string field
theory can be reduced to a commutative ring. From this viewpoint, Cardy states
can be identified with its idempotents. The algebra can be identified with a
fusion ring for...

We show that the boundary states satisfy a nonlinear relation (the
idempotency equation) with respect to the star product of closed string field
theory. This relation is universal in the sense that various D-branes,
including the infinitesimally d...

We show that the boundary states satisfy a nonlinear relation (the
idempotency equation) with respect to the star product of closed string field
theory. This relation is universal in the sense that various D-branes,
including the infinitesimally d...

We show that the boundary states are idempotent B*B=B with respect to the
star product of HIKKO type closed string field theory. Variations around the
boundary state correctly reproduce the open string spectrum with the gauge
symmetry. We explicit...

Using the Moyal star product, we define open bosonic string field theory
carefully, with a cutoff, for any number of string oscillators and any
oscillator frequencies. Through detailed computations, such as Neumann
coefficients for all string vert...

We give a detailed study of the associativity anomaly in open string field
theory from the viewpoint of the split string and Moyal formalisms. The origin
of the anomaly is reduced to the properties of the special infinite size
matrices which relat...

We study a matrix version of the purely cubic open string field theory as
describing the expansion around the closed string vacuum. Any D-branes in the
given closed string background can appear as classical solutions by using the
identity projecto...

We study a matrix version of the purely cubic open string field theory as
describing the expansion around the closed string vacuum. Any D-branes in the
given closed string background can appear as classical solutions by using the
identity projecto...

We study the identity projectors of the string field theory in the generic
BCFT background. We explain how it can be identified as the projector in the
linking algebra of the noncommutative geometry. We show that their
(regularized) trace is exact...

We give a comment on the possible role of the sliver state in the generic
boundary conformal field theory. We argue that for each Cardy state, there
exists at least one projector in the string field theory.

We construct the exact noncommutative solutions on tori. This gives an exact
description of tachyon condensation on bosonic D-branes, non-BPS D-branes and
brane-antibrane systems. We obtain various bound states of D-branes after the
tachyon conden...

Open string on symmetric product

International Journal of Modern Physics A16 557-608 2001