Matrix model with manifest general coordinate invariance

TL;DR

This paper develops a matrix model with manifest general coordinate invariance, reproducing Einstein gravity and proposing a supersymmetric extension that reduces to type IIB supergravity at low energies.

Contribution

It introduces a matrix model with manifest general coordinate invariance and explores its symmetry structure to recover gravity and supergravity in the classical limit.

Findings

Reproduces Einstein gravity in the low-energy limit

Proposes a supersymmetric matrix model reducing to type IIB supergravity

Analyzes symmetry mixing of Lorentz and gauge groups

Abstract

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.