Perturbative Analysis of Gauged Matrix Models

TL;DR

This paper explores how perturbative techniques in gauged matrix models can systematically compute non-perturbative aspects of supersymmetric gauge theories, including Seiberg-Witten solutions and superpotentials, even without exact solutions.

Contribution

It demonstrates the use of perturbative matrix model methods to derive non-perturbative gauge theory results, highlighting the role of ghost fields and formalism in these computations.

Findings

Perturbative matrix model techniques can compute non-perturbative gauge theory results.

Ghost fields are essential in the Feynman rules for vacua with broken gauge symmetry.

Systematic derivation of Seiberg-Witten and superpotential results from matrix model perturbation theory.

Abstract

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that non-perturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model/gauge theory (even though in some of these cases the exact answer can also be obtained by summing up planar diagrams of matrix models).