Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model

TL;DR

This paper uses a mean-field approximation of matrix integrals in the planar limit to derive the baryon and meson superpotential for SU(N) gauge theories, showing close agreement with traditional field theory results.

Contribution

It introduces a novel application of the mean-field approximation to matrix models for deriving gauge theory superpotentials, bridging matrix models and field theory.

Findings

Superpotential derived from matrix models closely matches field theory results.

Mean-field approximation effectively captures key features of gauge theories.

Planar limit assumption simplifies the derivation process.

Abstract

We discuss how to obtain the superpotential of the baryons and mesons for SU(N) gauge theories with N flavour matter fields from matrix integral. We apply the mean-field approximation for the matrix integral. Assuming the planar limit of the self-consistency equation, we show that the result almost agrees with the field theoretical result.