Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via dimensional reduction

TL;DR

This paper formulates 2D N=(2,2) super Yang-Mills theory on the lattice through dimensional reduction from 4D, employing specific fermion operators and ensuring a supersymmetric continuum limit despite lacking exact lattice supersymmetry.

Contribution

It introduces a lattice formulation of 2D N=(2,2) super Yang-Mills via dimensional reduction, with a focus on fermion operators and continuum limit properties.

Findings

Fermion determinant is real and semi-positive definite with overlap-Dirac operator.

Flat directions are compact, simplifying numerical integration.

Continuum limit is supersymmetric to all orders of perturbation theory.

Abstract

The N=(2,2) extended super Yang-Mills theory in 2 dimensions is formulated on the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory. We use the plaquette action for a bosonic sector and the Wilson- or the overlap-Dirac operator for a fermion sector. The fermion determinant is real and, moreover, when the overlap-Dirac operator is used, semi-positive definite. The flat directions in the target theory become compact and present no subtlety for a numerical integration along these directions. Any exact supersymmetry does not exist in our lattice formulation; nevertheless we argue that one-loop calculable and finite mass counter terms ensure a supersymmetric continuum limit to all orders of perturbation theory.