Progress in four-dimensional lattice supersymmetry

TL;DR

This paper reviews recent progress in formulating four-dimensional lattice supersymmetric theories, including super-QCD, N=4, and N=1 super-Yang-Mills, focusing on actions, counterterms, and fine-tuning requirements.

Contribution

It provides new lattice formulations for super-QCD and extends previous work on N=4 and N=1 super-Yang-Mills using Ginsparg-Wilson fermions, detailing fine-tuning needs.

Findings

Derived the number of fine-tunings needed for super-QCD with Ginsparg-Wilson fermions.

Presented general actions including counterterms for lattice super-QCD.

Extended formulations for N=4 and N=1 super-Yang-Mills on the lattice.

Abstract

We are entering an era where a number of large-scale lattice simulations of four-dimensional supersymmetric theories are under way. Moreover, proposals for how to approach such studies continue to progress. One particular line of research in this direction is described here. General actions for super-QCD, including counterterms required on the lattice, are given. We obtain the number of fine-tunings that is required, once gauge and flavor symmetries are accounted for, provided Ginsparg-Wilson fermions are used for the gauginos. We also review and extend our recent work on lattice formulations of N=4 super-Yang-Mills and N=1 super-Yang-Mills that exploit Ginsparg-Wilson fermions.