Supersymmetric lattices

TL;DR

This paper reviews recent advances in discretizing supersymmetric theories on lattices, highlighting new constructions that preserve some supersymmetries and maintain gauge invariance, enabling non-perturbative studies.

Contribution

It introduces a new class of lattice gauge theories with exact supersymmetry and gauge invariance, based on orbifold and topological field theory methods.

Findings

Lattice actions invariant under supersymmetry are constructed.

Theories are local, free of doublers, and gauge invariant.

Potential for non-perturbative analysis of supersymmetric theories.

Abstract

Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on ${\cal N}=4$ super Yang-Mills theory.