Yoshihisa Kitazawa

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.

Space-Time Structures from IIB Matrix Model.

We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite

IIB matrix model

N

Matrix models in homogeneous spaces

to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.

Ultraviolet stable fixed point and scaling relations in (2 + ϵ)-dimensional quantum gravity☆

We review our proposal for a constructive definition of superstring, type IIB matrix model. The IIB matrix model is a manifestly covariant model for space-time and matter which possesses N=2 supersymmetry in ten dimensions. We refine our arguments to reproduce string perturbation theory based on the loop equations. We emphasize that the space-time is dynamically determined from the eigenvalue distributions of the matrices. We also explain how matter, gauge fields and gravitation appear as fluctuations around dynamically determined space-time.

Quantum corrections on fuzzy sphere

Abstract We investigate noncommutative gauge theories in homogeneous spaces G / H . We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G . The isometry of a homogeneous space, G must be a subgroup of SO (10) in our construction. We investigate CP 2 = SU (3)/ U (2) case in detail which gives rise to 4-dimensional noncommutative gauge theory. We show that noncommutative gauge theory on R 4 can be realized in the large- N limit by letting the action approach IIB matrix model in a definite way. We discuss possible relevances of these theories to the large- N limit of IIB matrix model.

String field theory from IIB matrix model

Abstract We formulate a renormalizable quantum gravity in 2 + ϵ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range 0 c

String scale in noncommutative Yang–Mills

We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two-loop level. We find non-vanishing quantum corrections at each order even in supersymmetric models. In particular the two-loop contribution favors U(n) gauge group over U(1) contrary to the tree action in a deformed IIB matrix model with a Myers term. We further observe close correspondences to 2-dimensional quantum gravity.