First results from simulations of supersymmetric lattices

TL;DR

This paper presents pioneering numerical simulations of lattice theories with exact supersymmetry, exploring their stability, spectra, and supersymmetry breaking, indicating potential for simulating ${ m N}=4$ super Yang-Mills.

Contribution

First numerical simulations of supersymmetric lattice theories from orbifold constructions, analyzing stability, spectra, and supersymmetry breaking effects.

Findings

U(N) theories lack non-perturbative stable vacua

Truncation to SU(N) stabilizes vacua

Results suggest ${ m N}=4$ super Yang-Mills simulations are feasible

Abstract

We conduct the first numerical simulations of lattice theories with exact supersymmetry arising from the orbifold constructions of \cite{Cohen:2003xe,Cohen:2003qw,Kaplan:2005ta}. We consider the $\cQ=4$ theory in $D=0,2$ dimensions and the $\cQ=16$ theory in $D=0,2,4$ dimensions. We show that the U(N) theories do not possess vacua which are stable non-perturbatively, but that this problem can be circumvented after truncation to SU(N). We measure the distribution of scalar field eigenvalues, the spectrum of the fermion operator and the phase of the Pfaffian arising after integration over the fermions. We monitor supersymmetry breaking effects by measuring a simple Ward identity. Our results indicate that simulations of ${\cal N}=4$ super Yang-Mills may be achievable in the near future.