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Approximations for strongly-coupled supersymmetric quantum mechanics

Daniel Kabat·Gilad Lifschytz
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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.

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Daniel Kabat, Gilad Lifschytz. 2000-01-05. Approximations for strongly-coupled supersymmetric quantum mechanics. https://doi.org/10.1016/s0550-3213(99)00818-4

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