Notes on (twisted) lattice supersymmetry

TL;DR

This paper introduces a novel lattice discretization method for supersymmetric theories using twisted formulations, which preserve a scalar supercharge as an exact symmetry on the lattice, applicable to various models.

Contribution

It proposes a new approach to lattice supersymmetry by discretizing twisted formulations that maintain a scalar supercharge as an exact lattice symmetry.

Findings

Successfully applied to quantum mechanics, sigma models, and Yang-Mills theories

Preserves a scalar nilpotent supercharge exactly on the lattice

Simplifies the implementation of supersymmetry in lattice models

Abstract

We describe a new approach to the problem of putting supersymmetric theories on the lattice. The basic idea is to discretize a {\it twisted} formulation of the supersymmetric theory. For certain theories with extended supersymmetry these twisted formulations contain only integer spin fields. The twisting exposes a scalar nilpotent supercharge which generates an exact lattice symmetry. We gives examples from quantum mechanics, sigma models and Yang-Mills theories.