Relations among Supersymmetric Lattice Gauge Theories via Orbifolding

TL;DR

This paper presents a method to derive supersymmetric lattice gauge theories from orbifolding and deconstruction, revealing complexified models with preserved supersymmetries and enabling the construction of new lattice theories.

Contribution

It introduces a general orbifolding-based approach to derive supersymmetric lattice theories, including complexified models and their truncations, applicable to various dimensions.

Findings

Catterall's 2D N=(2,2) model has two preserved supersymmetries.

The construction can produce new supersymmetric lattice theories.

A connection to Sugino's 4D N=2 lattice formulation is established.

Abstract

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash between charge assignments under U(1)-symmetries and lattice assignments in terms of scalar, vector and tensor components for the fermions. Other prescriptions for how to discretize the theory follow automatically by orbifolding and deconstruction. We find that Catterall's complexified model for the two-dimensional N=(2,2) theory has two independent preserved supersymmetries. We comment on consistent truncations to lattice theories without this complexification and with the correct continuum limit. The construction of lattice theories this way is general, and can be used to derive new supersymmetric lattice theories through the orbifolding procedure. As an example, we apply the prescription to topologically twisted four-dimensional N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is closely related to the lattice formulation previously given by Sugino.