Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry

TL;DR

This paper develops a lattice formulation for 2D N=(2,2) supersymmetric QCD using the Ginsparg-Wilson relation, enabling exact chiral symmetry and supercharge preservation on the lattice.

Contribution

It introduces the overlap Dirac operator into 2D N=(2,2) SQCD, allowing for exact lattice chiral symmetry and supercharge preservation, and extends to models with general matter content.

Findings

Exact chiral flavor symmetry realized on the lattice.

Lattice actions for general matter multiplets constructed.

Superpotential terms incorporated with holomorphic structure.

Abstract

In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N=(2,2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U(1) (the overall U(1)) of the gauge group G=U(N), and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.