DV and WDVV

TL;DR

This paper proves that the quasiclassical tau-function associated with multi-support matrix model solutions satisfies the Witten-Dijkgraaf-Verlinde-Verlinde equations, linking matrix models to supersymmetric gauge theories.

Contribution

It establishes a mathematical connection between matrix model tau-functions and WDVV equations, supporting the Dijkgraaf-Vafa conjecture.

Findings

Proves the tau-function satisfies WDVV equations

Links matrix models to supersymmetric gauge theories

Supports Dijkgraaf-Vafa proposal

Abstract

We prove that the quasiclassical tau-function of the multi-support solutions to matrix models, proposed recently by Dijkgraaf and Vafa to be related to the Cachazo-Intrilligator-Vafa superpotentials of the N=1 supersymmetric Yang-Mills theories, satisfies the Witten-Dijkgraaf-Verlinde-Verlinde equations.