A Method for Measuring the Witten Index Using Lattice Simulation

Abstract

We propose a method to measure the Witten index using lattice simulation. A requirement for the lattice model is that it has at least one exact supersymmetry at finite lattice spacing. We prove the validity of the method in case of the supersymmetric quantum mechanics, where the index is well known.

23 pages, 9 figures; v2: references revised, section 2 improved and fig. 3 updated; v3: a version to appear in NPB

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Cited by in corpus (12)

• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
• Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
• Supersymmetric quantum mechanics on the lattice: II. Exact results
• Direct computational approach to lattice supersymmetric quantum mechanics
• Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
• Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• Simple Models in Supersymmetric Quantum Mechanics on a Graph
• Analytic calculation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics
• Witten index from lattice simulation