Supersymmetric lattices - a brief introduction

TL;DR

This paper reviews recent advances in constructing lattice actions that preserve supersymmetry, gauge invariance, and are free of doublers, focusing on ${ m N}=4$ super Yang-Mills theory.

Contribution

It introduces new theoretical methods for creating supersymmetric lattice actions that maintain key symmetries and avoid common lattice issues.

Findings

Lattice actions can be explicitly invariant under supersymmetry.

Theories are local and free of fermion doubling.

Exact gauge invariance is maintained in ${ m N}=4$ super Yang-Mills.

Abstract

Recently, new theoretical ideas have allowed the construction of lattice actions which are explicitly invariant under one or more supersymmetries. These theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In this talk these ideas are reviewed with particular emphasis being placed on ${\cal N}=4$ super Yang-Mills theory.