Field Equations of Massless Fields in the New Interpretation of the Matrix Model

TL;DR

This paper extends a matrix model interpretation to include torsion, linking certain torsion components to string theory fields and exploring matrix models with additional terms that satisfy string equations of motion.

Contribution

It generalizes the matrix model approach to covariant derivatives with torsion and identifies some torsion components with string theory fields.

Findings

Some torsion components correspond to string theory fields like the dilaton and B-field.

Matrix models with mass or cubic terms satisfy string theory equations of motion.

The approach broadens the connection between matrix models and string theory.

Abstract

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the $B$-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.