Supersymmetry on the lattice and the status of the Super-Yang-Mills simulations

TL;DR

This paper reviews the challenges of implementing supersymmetry on the lattice, discusses approaches like Ginsparg-Wilson relations, and provides an update on recent supersymmetric Yang-Mills simulations.

Contribution

It summarizes the current status of lattice supersymmetry, including theoretical difficulties and recent simulation progress in supersymmetric Yang-Mills theories.

Findings

Supersymmetry cannot be locally realized on the lattice.

Ginsparg-Wilson relation offers a potential solution but remains incomplete.

Recent simulations of SYM are advancing despite theoretical challenges.

Abstract

Supersymmetry (SUSY) and supersymmetric field theories are an interesting topic for numerical lattice simulations. Similar to the chiral symmetry there is also no local realization of (interacting) supersymmetry on the lattice. I briefly review the basic reasons for the breaking of supersymmetry. One attempt to solve the problem uses a Ginsparg-Wilson relation for supersymmetry. However, apart from the free theory, a solution of this relation has so far not been found. For supersymmetric Yang-Mills (SYM) theory a fine-tuning of the bare gluino mass is enough to arrive at a supersymmetric continuum limit. The last part of this work contains a short status report of recent SYM simulations.