Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist

TL;DR

This paper develops a lattice formulation for 2D $ abla(2,2)$ SQCD that preserves some supersymmetry and avoids common lattice issues, enabling continuum limit realization without fine tuning.

Contribution

It introduces a simple lattice construction for 2D $ abla(2,2)$ SQCD with exact supersymmetry preservation and addresses lattice artifacts without admissibility conditions.

Findings

Preserves one supercharge exactly on the lattice

Avoids species doubling without admissibility

Ensures correct continuum limit without fine tuning

Abstract

We present a simple lattice formulation of two-dimensional $\mathcal{N}=(2,2)$ $U(k)$ supersymmetric QCD (SQCD) with $N$ matter multiplets in the fundamental representation. The construction uses compact gauge link variables and exactly preserves one linear combination of supercharges on the two-dimensional regular lattice. Artificial saddle points in the weak coupling limit and the species doubling are evaded without imposing the admissibility. A perturbative power-counting argument indicates that the target supersymmetric theory is realized in the continuum limit without any fine tuning.