Lifting flat directions in lattice supersymmetry

TL;DR

This paper introduces a method to lift flat directions in lattice supersymmetric Yang--Mills theory without breaking supersymmetry, significantly improving numerical simulations and convergence to the continuum limit.

Contribution

It proposes a novel procedure to lift U(1) flat directions in lattice $\\mathcal{N} = 4$ SYM while preserving exact supersymmetry, enhancing computational accuracy.

Findings

Reduced violations of supersymmetric Ward identities

Faster approach to the continuum limit in simulations

Improved lattice action stability

Abstract

We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the exact lattice supersymmetry. The basic idea is to modify the equations of motion of an auxiliary field, which determine the moduli space of the system. Applied to numerical calculations, the resulting improved lattice action leads to dramatically reduced violations of supersymmetric Ward identities and much more rapid approach to the continuum limit.