A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry

TL;DR

This paper develops lattice formulations of super Yang-Mills theories with extended supersymmetry, maintaining exact supersymmetry and enabling continuum limits without fine tuning for certain models.

Contribution

It introduces a lattice approach that preserves some supersymmetry exactly, facilitating nonperturbative studies of super Yang-Mills theories.

Findings

Exact supersymmetry is maintained on the lattice.

Continuum theories are recovered without fine tuning for specific models.

The approach applies to multiple dimensions and supersymmetry extensions.

Abstract

We construct super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. Gauge fields are represented by ordinary unitary link variables, and the exact supercharges are nilpotent up to gauge transformations. Among the models, we show that the desired continuum theories are obtained without any fine tuning of parameters for the cases ${\cal N}=2, 4, 8$ in two-dimensions.