Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation

TL;DR

This paper develops a lattice formulation for two-dimensional N=(2,2) supersymmetric gauge theory with fundamental matter fields, demonstrating equivalence between orbifolding and geometrical discretization methods.

Contribution

It introduces a novel lattice construction for supersymmetric gauge theories with matter, showing the equivalence of two discretization schemes.

Findings

Lattice formulation successfully incorporates matter fields in the fundamental representation.

Orbifolding and geometrical discretization methods yield equivalent lattice models.

The approach preserves supersymmetry on the lattice.

Abstract

In this paper, we construct a lattice formulation for two-dimensional N=(2,2) supersymmetric gauge theory with matter fields in the fundamental representation. We first construct it by the orbifolding procedure from Yang-Mills matrix theory with eight supercharges. We show that we can obtain the same lattice formulation by extending the geometrical discretization scheme. This suggests that the equivalence between the two schemes holds even for theories with matter fields.