Geometry of Orbifolded Supersymmetric Lattice Gauge Theories

TL;DR

This paper demonstrates that orbifolding and deconstruction methods for constructing supersymmetric lattice gauge theories are equivalent to Catterall's geometrical discretization, and extends its applicability to more general theories.

Contribution

It proves the equivalence of two prominent lattice construction methods and broadens the scope of geometrical discretization for supersymmetric theories.

Findings

Orbifolding and deconstruction lead to Catterall's discretization.

Both methods produce identical lattice discretizations for p-form theories.

Geometrical discretization can be applied to more general theories.

Abstract

We prove that the prescription for construction of supersymmetric lattice gauge theories by orbifolding and deconstruction directly leads to Catterall's geometrical discretization scheme in general. These two prescriptions always give the same lattice discretizations when applied to theories of p-form fields. We also show that the geometrical discretization scheme can be applied to more general theories.