Lattice N=4 three-dimensional super-Yang-Mills

TL;DR

This paper discusses the lattice formulation of N=4 three-dimensional super-Yang-Mills, focusing on supersymmetry restoration, counterterm calculations, and motivations like mirror symmetry and holography.

Contribution

It compares different lattice formulations based on the Donaldson-Witten and Blau-Thompson twists, identifying a key counterterm for supersymmetry restoration.

Findings

Single counterterm needed for supersymmetry restoration

Two-loop lattice perturbation theory computes the counterterm

Model is super-renormalizable in three dimensions

Abstract

We describe our recent work on the lattice formulation of N=4 three-dimensional super-Yang-Mills. Our formulation was based on the Donaldson-Witten twist, but we have also been studying the formulation based on the Blau-Thompson twist by Joseph. We find in the latter case there is a single counterterm necessary to restore supersymmetry in the continuum limit, and that this counterterm can be computed with a two-loop calculation in lattice perturbation theory. It is crucial that this three-dimensional model is super-renormalizable. We also describe some of the motivations for studying three-dimensional theories, including mirror symmetry and holographic cosmology.