Numerical approach to SUSY quantum mechanics and the gauge/gravity duality

Abstract

We demonstrate that Monte-Carlo simulation is a practical tool to study nonperturbative aspects of supersymmetric quantum mechanics. As an example we study D0-brane quantum mechanics in the context of superstring theory. Numerical data nicely reproduce predictions from gravity side, including the coupling constant dependence of the string alpha' correction. This strongly suggests the duality to hold beyond the supergravity approximation. Although detail of the stringy correction cannot be obtained by state-of-the-art techniques in gravity side, in the matrix quantum mechanics we can obtain concrete values. Therefore the Monte-Carlo simulation combined with the duality provides a powerful tool to study the superstring theory.

16 pages, 4 figures. Based on an invited talk at the workshop "Supersymmetric Quantum Mechanics and Spectral Design", Benasque, Spain, 2010, Jul 18 -- Jul 30

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