Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models

TL;DR

This paper extends the Dijkgraaf-Vafa matrix model to five-dimensional gauge theories compactified to four dimensions, connecting it with elliptic superpotentials and integrable systems, providing new insights into 5D gauge dynamics.

Contribution

It introduces a quantum mechanical matrix model approach to describe five-dimensional gauge theories and links it with elliptic superpotentials and integrable systems.

Findings

Derived superpotential expressions match elliptic superpotential approach.

Connected matrix model results with Nekrasov's 5D Seiberg-Witten theory.

Established equivalence with relativistic elliptic Calogero-Moser system.

Abstract

We show how the Dijkgraaf-Vafa matrix model proposal can be extended to describe five-dimensional gauge theories compactified on a circle to four dimensions. This involves solving a certain quantum mechanical matrix model. We do this for the lift of the N=1* theory to five dimensions. We show that the resulting expression for the superpotential in the confining vacuum is identical with the elliptic superpotential approach based on Nekrasov's five-dimensional generalization of Seiberg-Witten theory involving the relativistic elliptic Calogero-Moser, or Ruijsenaars-Schneider, integrable system.