Exact Superpotentials from Matrix Models

TL;DR

This paper tests Dijkgraaf and Vafa's conjecture that superpotentials in certain SUSY gauge theories can be derived from matrix models, confirming the proposal through comparison with known results and extending it to Leigh-Strassler deformations.

Contribution

The paper provides a detailed verification of the DV conjecture for N=4 SUSY Yang-Mills deformations and extends the approach to Leigh-Strassler deformations, demonstrating its broad applicability.

Findings

Complete agreement between matrix model predictions and gauge theory results.

Extraction of exact eigenvalues of the adjoint scalar in the confining vacuum.

Extension of the method to Leigh-Strassler deformations.

Abstract

Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory.