From Twisted Supersymmetry to Orbifold Lattices

TL;DR

This paper demonstrates how to derive supersymmetric orbifold lattice models from twisted supersymmetric Yang-Mills theories, maintaining gauge invariance and exact supersymmetry at finite lattice spacing.

Contribution

It provides a direct discretization method for supersymmetric orbifold lattices from twisted theories, clarifying their relation to continuum supersymmetric Yang-Mills theories.

Findings

Derived orbifold lattices from twisted theories.

Maintained one exact supersymmetry on the lattice.

Connected lattice models to continuum Marcus twist of ${\cal N}=4$ Yang-Mills.

Abstract

We show how to derive the supersymmetric orbifold lattices of Cohen et al. \cite{Cohen:2003xe,Cohen:2003qw} and Kaplan et al. \cite{Kaplan:2005ta} by direct discretization of an appropriate twisted supersymmetric Yang-Mills theory. We examine in detail the four supercharge two dimensional theory and the theory with sixteen supercharges in four dimensions. The continuum limit of the latter theory is the well known Marcus twist of ${\cal N}=4$ Yang-Mills. The lattice models are gauge invariant and possess one exact supersymmetry at non-zero lattice spacing.