Supersymmetry on the lattice

TL;DR

This paper reviews the development and current status of lattice formulations for supersymmetric gauge theories, specifically ${ m N}=1$ and ${ m N}=4$ super Yang-Mills, highlighting challenges, progress, and future directions.

Contribution

It provides a comprehensive overview of lattice approaches to supersymmetric theories, summarizing formal developments and recent results in the field.

Findings

Progress in formulating ${ m N}=1$ and ${ m N}=4$ super Yang-Mills on the lattice

Current results demonstrating partial preservation of supersymmetry

Identification of key challenges and future research directions

Abstract

We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.