Approximations for strongly-coupled supersymmetric quantum mechanics

We advocate a set of approximations for studying the finite temperature beh avior of strongly-coupled theories in 0 + 1 dimensions. The approximation c onsists of expanding about a Gaussian action, with the width of the Gaussia n 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 plan ar contribution to the gap equations. We analyze several models of scalar supersymmetric quantum mechanics, and s how that the Gaussian approximation correctly distinguishes between a modul i space, mass gap, and supersymmetry breaking at strong coupling. Then we a pply the approximation to a bosonic large-hi gauge theory, and argue that a Gross-Witten transition separates the weak-coupling and strong-coupling re gimes. A similar transition should occur in a generic large-N gauge theory, in particular in 0-brane quantum mechanics. (C) 2000 Elsevier Science B.V. All rights reserved.