Exact lattice supersymmetry

TL;DR

This paper reviews recent lattice formulations of supersymmetric theories that preserve some supersymmetry at finite lattice spacing, focusing on methods, equivalences, and implications for continuum limits.

Contribution

It introduces and compares twisted and orbifold-deconstruction approaches for lattice supersymmetry, highlighting their equivalence and benefits in reducing fine-tuning.

Findings

Exact lattice supersymmetry reduces fine-tuning requirements.

Equivalence of twisted and orbifold methods demonstrated.

Framework applicable to ${\cal N}=4$ SYM in four dimensions.

Abstract

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of ${\cal N}=4$ SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.