A lattice path integral for supersymmetric quantum mechanics

TL;DR

This paper presents a lattice path integral approach for supersymmetric quantum mechanics, demonstrating exact supersymmetry at finite lattice spacing and continuum limit restoration without fine tuning.

Contribution

It introduces a non-standard lattice action with exact supersymmetry at zero interaction and shows how to achieve local supersymmetry with minimal modifications.

Findings

Mass gaps measured with better than 1% precision

Supersymmetry is preserved in the continuum limit with the new action

Standard lattice actions fail to restore supersymmetry at zero lattice spacing

Abstract

We report on a study of the supersymmetric anharmonic oscillator computed using a euclidean lattice path integral. Our numerical work utilizes a Fourier accelerated hybrid Monte Carlo scheme to sample the path integral. Using this we are able to measure massgaps and check Ward identities to a precision of better than one percent. We work with a non-standard lattice action which we show has an {\it exact} supersymmetry for arbitrary lattice spacing in the limit of zero interaction coupling. For the interacting model we show that supersymmetry is restored in the continuum limit without fine tuning. This is contrasted with the situation in which a `standard' lattice action is employed. In this case supersymmetry is not restored even in the limit of zero lattice spacing. Finally, we show how a minor modification of our action leads to an {\it exact}, local lattice supersymmetry even in the presence of interaction.