Approximations for strongly-coupled supersymmetric quantum mechanics

Daniel Kabat, Gilad Lifschytz

Research output: Contribution to journalArticlepeer-review


We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0q 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-TV 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, q 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)419-456
Number of pages38
JournalNuclear Physics B
Issue number1-2
StatePublished - 3 Apr 2000
Externally publishedYes

Bibliographical note

Funding Information:
We are grateful to Stanley Deser, Misha Fogler, Gerry Guralnik, Roman Jackiw, Anton Kapustin, David Lowe, Samir Mathur, Emil Mottola, Martin Schaden, Vipul Periwal, Marc Spiegelman, Paul Townsend and Daniel Zwanziger for valuable discussions. DK wishes to thank NYU for hospitality while this work was in progress. The work of DK is supported by the DOE under contract DE-FG02-90ER40542 and by the generosity of Martin and Helen Chooljian. GL wishes to thank the Aspen Center for Physics for hospitality while this work was in progress. The work of GL is supported by the NSF under grant PHY-98-02484.


  • Black holes in string theory
  • D-branes
  • Strongly-coupled gauge theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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