Symmetries of Large N Matrix Models for Closed Strings

TL;DR

This paper uncovers the symmetry algebra of large N multi-matrix models and links them to quantum spin chains, enabling exact solutions for some models using known spin chain results.

Contribution

It introduces the symmetry algebra of large N matrix models and connects them to solvable quantum spin chains, providing new exact solutions.

Findings

Identified the symmetry algebra of multi-matrix models in the large N limit.

Established a correspondence between matrix models and quantum spin chains.

Solved specific multi-matrix models exactly using spin chain techniques.

Abstract

We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known results of solvable spin chain systems.