Twisted supersymmetric sigma model on the lattice

TL;DR

This paper numerically investigates a lattice formulation of the twisted supersymmetric O(3) sigma model, demonstrating supersymmetry restoration in the continuum limit and exploring potential terms and discretization approaches.

Contribution

It introduces a lattice formulation based on twisting that preserves a nilpotent supercharge and shows supersymmetry restoration without fine tuning.

Findings

Supersymmetry is restored in the continuum limit.

Potential terms can preserve supersymmetry on the lattice.

A non-zero chiral condensate consistent with instanton effects is observed.

Abstract

In this paper we conduct a numerical study of the supersymmetric O(3) non-linear sigma model. The lattice formulation we employ was derived in \cite{sigma1} and corresponds to a discretization of a {\it twisted} form of the continuum action. The twisting process exposes a {\it nilpotent} supercharge $Q$ and allows the action to be rewritten in $Q$-exact form. These properties may be maintained on the lattice. We show how to deform the theory by the addition of potential terms which preserve the supersymmetry. A Wilson mass operator may be introduced in this way with a minimal breaking of supersymmetry. We additionally show how to rewrite the theory in the language of K\"{a}hler-Dirac fields and explain why this avenue does not provide a good route to discretization. Our numerical results provide strong evidence for a restoration of full supersymmetry in the continuum limit {\it without} fine tuning. We also observe a non-vanishing chiral condensate as expected from continuum instanton calculations.