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Takehiro Azuma

Publications and source records attributed to Takehiro Azuma.

43 records · Page 3Linked to original sources
arXiv2004

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated even for finite matrix size, and in the case of $k$ coincident fuzzy spheres it gives rise to a regularized U($k$) gauge theory on a noncommutative geometry. Here we study the matrix model nonperturbatively by Monte Carlo simulation. The system undergoes a first order phase transition as we change the coefficient ($α$) of the Chern-Simons term. In the small $α$ phase, the large $N$ properties of the system are qualitatively the same as in the pure Yang-Mills model ($α=0$), whereas in the large $α$ phase a single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are observed as meta-stable states, and we argue in particular that the $k$ coincident fuzzy spheres cannot be realized as the true vacuum in this model even in the large $N$ limit. We also perform one-loop calculations of various observables for arbitrary $k$ including $k=1$. Comparison with our Monte Carlo data suggests that higher order corrections are suppressed in the large $N$ limit.

hep-th↗
arXiv2004

Matrix models and the gravitational interaction

The large-N reduced models have been proposed as the nonperturbative formulation of the superstring theory. One of the most promising candidates is the IIB matrix model. While there have been a lot of interesting discoveries of the IIB matrix model in relation to the gravity, we have a lot of problems to surmount, if a large-N reduced model is to be an eligible framework to unify the gravitational interaction. Firstly, it is still an enigma how we can realize the local Lorentz invariant matrix model. In addition, we need to understand how we can describe the curved spacetime more manifestly, in terms of a large-N reduced model. This thesis discusses several attempts to address these issues concerning the gravitational interaction. This thesis is based on the following author's works hep-th/0102168, hep-th/0204078, hep-th/0209057 and hep-th/0401038.

hep-th↗
arXiv2003

Investigation of Matrix Theory via Super Lie Algebra

This paper reports the investigation of a matrix model via super Lie algebra, following the proposal of L. Smolin. We consider the osp(1|32,R) nongauged matrix model and gl(1|32,R) gauged matrix model, especially paying attention to the supersymmetry and the relationship with IKKT model. This paper is based on the collaboration with the collaboration with S.Iso, H.Kawai and Y.Ohwashi.

hep-th↗
arXiv2002

Curved-space classical solutions of a massive supermatrix model

We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(1|32,R), which could play a role in the construction of the eleven-dimensional M-theory. This model contains a massive version of the IIB matrix model, where some fields have a tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable. However, this model possesses several classical solutions where these fields build noncommutative curved spaces and these solutions are shown to be energetically more favorable than the trivial vacuum. In particular, we describe in details two cases, the SO(3) \times SO(3) \times SO(3) (three fuzzy 2-spheres) and the SO(9) (fuzzy 8-sphere) classical backgrounds.

hep-th↗
arXiv2002

Matrix model with manifest general coordinate invariance

We present a formulation of a matrix model which manifestly possesses the general coordinate invariance when we identify the large $N$ matrices with differential operators. In order to build a matrix model which has the local Lorentz invariance, we investigate how the $so(9,1)$ Lorentz symmetry and the $u(N)$ gauge symmetry are mixed together. We first analyze the bosonic part of the model, and we find that the Einstein gravity is reproduced in the classical low-energy limit. And we present a proposal to build a matrix model which has ${\cal N}=2$ SUSY and reduces to the type IIB supergravity in the classical low-energy limit.

hep-th↗
arXiv2001

Supermatrix Models

We investigate several matrix models based on super Lie algebras, osp(1|32,R), u(1|16,16) and gl(1|32,R). They are natural generalizations of IIB matrix model and were first proposed by Smolin. In particular, we study the supersymmetry structures of these models and discuss possible reductions to IIB matrix model. We also point out that diffeomorphism invariance is hidden in gauge theories on noncommutative space which are derived from matrix models. This symmetry is independent of the global SO(9,1) invariance in IIB matrix model and we report our trial to extend the global Lorentz invariance to local symmetry by introducing u(1|16,16) or gl(1|32,R) super Lie algebras.

hep-th↗