Approximations for strongly-coupled supersymmetric quantum mechanics

TL;DR

This paper introduces a Gaussian approximation method for analyzing the finite temperature behavior of strongly-coupled supersymmetric quantum mechanics, effectively distinguishing different phases and transitions.

Contribution

It develops a superspace-based Gaussian approximation applicable to large-N theories, providing insights into phase transitions and supersymmetry breaking.

Findings

Gaussian approximation distinguishes moduli space, mass gap, and SUSY breaking.

Identifies a Gross-Witten transition in large-N gauge theories.

Applicable to supersymmetric and bosonic models at strong coupling.

Abstract

We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a set of gap equations. The approximation can be applied to supersymmetric systems, provided that the gap equations are formulated in superspace. It can be applied to large-N theories, by keeping just the planar contribution to the gap equations. We analyze several models of scalar supersymmetric quantum mechanics, and show that the Gaussian approximation correctly distinguishes between a moduli space, mass gap, and supersymmetry breaking at strong coupling. Then we apply the approximation to a bosonic large-N gauge theory, and argue that a Gross-Witten transition separates the weak-coupling and strong-coupling regimes. A similar transition should occur in a generic large-N gauge theory, in particular in 0-brane quantum mechanics.