M-Theory of Matrix Models

TL;DR

This paper proposes a unifying M-theory framework for eigenvalue matrix models, linking different models and dualities, and drawing analogies with Yang-Mills theory instanton decompositions.

Contribution

It introduces an M-theory perspective that unifies various eigenvalue matrix models and their dualities, including Dijkgraaf-Vafa and Kontsevich tau-functions.

Findings

Unified description of matrix models via M-theory

Identification of dualities analogous to Yang-Mills decompositions

Connections between different matrix model branches

Abstract

Small M-theories unify various models of a given family in the same way as the M-theory unifies a variety of superstring models. We consider this idea in application to the family of eigenvalue matrix models: their M-theory unifies various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition functions) with Kontsevich tau-function. Moreover, the corresponding duality relations look like direct analogues of instanton and meron decompositions, familiar from Yang-Mills theory.