Lattice N=4 super Yang-Mills at Strong Coupling

TL;DR

This study uses a new lattice action to numerically simulate N=4 super Yang-Mills theory at strong coupling, providing evidence of no sign problem and results consistent with holographic predictions.

Contribution

The paper introduces a novel lattice action that overcomes previous sign problem issues, enabling simulations of N=4 super Yang-Mills at strong coupling.

Findings

No sign problem observed in simulations.

The supersymmetric Wilson loop scales as the square root of the 't Hooft coupling.

The theory remains in a single phase across the studied coupling range.

Abstract

In this paper we present results from numerical simulations of N=4 super Yang-Mills for two color gauge theory over a wide range of 't Hooft coupling $0<\lambda\le 30$ using a supersymmetric lattice action \cite{Catterall:2009it}. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just $SU(2)$ rather than $U(2)$ gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the 't Hooft coupling $\lambda$ for large $\lambda$ in agreement with holographic predictions.