3d N=4 Super-Yang-Mills on a Lattice

TL;DR

This paper introduces a novel lattice formulation for three-dimensional N=4 super-Yang-Mills by complexifying a four-dimensional twist, ensuring gauge invariance and analyzing its continuum limit.

Contribution

It presents a new approach to discretizing 3D N=4 super-Yang-Mills via complexification of a 4D twist, enabling lattice gauge invariance and continuum limit analysis.

Findings

Lattice gauge invariance constrains the model to three dimensions.

Uncomplexified 3D N=4 super-Yang-Mills can be obtained in the continuum limit.

The approach allows for controlled renormalization and mass term adjustments.

Abstract

In this paper we explore a new approach to studying three-dimensional N=4 super-Yang-Mills on a lattice. Our strategy is to complexify the Donaldson-Witten twist of four-dimensional N=2 super-Yang-Mills to make it amenable to a lattice formulation and we find that lattice gauge invariance forces the model to live in at most three dimensions. We analyze the renormalization of the lattice theory and show that uncomplexified three-dimensional N=4 super-Yang-Mills can be reached in the continuum limit by supplementing the lattice action with appropriate mass terms.