A Method for Measuring the Witten Index Using Lattice Simulation

TL;DR

This paper introduces a lattice simulation method to measure the Witten index, requiring models with exact supersymmetry at finite lattice spacing, validated through supersymmetric quantum mechanics.

Contribution

It presents a novel lattice-based approach for calculating the Witten index, extending computational tools for supersymmetric theories.

Findings

Method validated for supersymmetric quantum mechanics

Accurate measurement of the Witten index demonstrated

Applicable to models with exact supersymmetry at finite lattice spacing

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.