N=4 Supersymmetry on a Space-Time Lattice

TL;DR

This paper develops a lattice formulation of maximally supersymmetric Yang--Mills theory in four dimensions that preserves some supersymmetry and investigates its behavior at strong coupling, addressing lattice artifacts.

Contribution

It provides a detailed lattice formulation of N=4 supersymmetric Yang--Mills theory that preserves a single supersymmetry and analyzes how to remove artifacts from U(N) to SU(N) at strong coupling.

Findings

Lattice artifacts from U(1) degrees of freedom can be removed.

The SU(N) lattice theory exhibits expected conformal behavior.

The formulation is valid in both weak and strong coupling regimes.

Abstract

Maximally supersymmetric Yang--Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N), the lattice formulation is naturally described in terms of gauge group U(N). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N) gauge group with the expected apparently conformal behavior at both weak and strong coupling.