Supersymmetric quantum mechanics on the lattice: II. Exact results

TL;DR

This paper presents exact analytical results for ${ m N}=2$ supersymmetric quantum mechanics on the lattice, analyzing key observables like the Witten index, mass spectra, and Ward identities using transfer matrix methods.

Contribution

It provides the first exact solutions at finite lattice spacing for supersymmetric quantum mechanics formulated with bosonic and fermionic bonds.

Findings

Exact calculation of the Witten index.

Determination of the mass spectra.

Verification of Ward identities.

Abstract

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper -- the second in a series of three -- we present such an investigation for ${\cal N}=2$ supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.