Nobuyuki Ishibashi

A Large-N Reduced Model as Superstring

Abstract A matrix model which has the manifest ten-dimensional N = 2 super Poincare invariance is proposed. Interactions between BPS-saturated states are analyzed to show that the massless spectrum is the same as that of type IIB string theory. It is conjectured that the large- N reduced model of ten-dimensional super Yang-Mills theory can be regarded as a constructive definition of this model and therefore is equivalent to superstring theory.

Non-commutative Yang–Mills in IIB matrix model

Abstract We show that twisted reduced models can be interpreted as non-commutative Yang–Mills theory. Based upon this correspondence, we obtain non-commutative Yang–Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of non-commutative Yang–Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.

Wilson loops in non-commutative Yang–Mills

Abstract We study the correlation functions of the Wilson loops in non-commutative Yang–Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the non-commutativity scale. At large momentum scale, the Wilson loops in non-commmutative Yang–Mills represent extended objects. They coincide with those in ordinary Yang–Mills theory in a low energy limit. The correlation functions on D-branes in a IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.

String field theory of c ⩽ 1 noncritical strings

We construct a string field Hamiltonian for a noncritical string theory with the continuum limit of the Ising model or its generalization as the matter theory on the worldsheet. It consists of only three string vertices as in the case for

A Relation Between Commutative and Noncommutative Descriptions of D-Branes

c=0

p-Branes from (p − 2)-branes in bosonic string theory

. We also discuss a general consistency condition that should be satisfied by this kind of string field Hamiltonian.We construct a string field Hamiltonian for a noncritical string theory with the continuum limit of the Ising model or its generalization as the matter theory on the worldsheet. It consists of only three string vertices as in the case for

String scale in noncommutative Yang–Mills

c=0

Path integral approach to string theory on AdS3

. We also discuss a general consistency condition that should be satisfied by this kind of string field Hamiltonian.

A Background independent formulation of noncritical string theory

In string theory, D-branes can be expressed as a configuration of infinitely many lower dimensional D-branes. Using this relation, the worldvolume theory of D-branes can be regarded as the worldvolume theory of the infinitely many lower dimensional branes. In the description in terms of the lower dimensional branes, some of the worldvolume coordinates become noncommutative. Actually this noncommutative theory can be regarded as noncommutative Yang-Mills theory. Therefore the worldvolume theory of D-branes have two equivalent descriptions, namely the usual static gauge description using ordinary Yang-Mills theory and the noncommutative description using noncommutative Yang-Mills theory. It will be shown that these two descriptions correspond to two different ways of gauge fixing of the reparametrization invariance and its generalization. We will give an explicit relation between commutative gauge field and noncommutative gauge field in semiclassical approximation, when the gauge group is U(1).

Two-dimensional quantum gravity in temporal gauge

We show that the Dirichlet p-brane can be expressed as a configuration of infinitely many Dirichlet (p − 2)-branes in the bosonic string theory. Using this fact, we interpret the massless fields on the p-brane world-volume as deformations of the configuration of the (p − 2)-branes. In particular we find that the world-volume gauge field parametrizes part of the group of diffeomorphisms on the world-volume.