Investigations of supersymmetric Yang--Mills theories

TL;DR

This paper reports on lattice studies of supersymmetric Yang--Mills theories in 3d and 4d, validating computational methods and exploring non-perturbative properties like running couplings and beta functions.

Contribution

It introduces new lattice investigations of SYM theories, validates phase-quenched RHMC calculations, and develops software for supersymmetric QCD simulations.

Findings

Fermion pfaffian is approximately real and positive in 3d SYM with 16 supercharges

Initiated studies of running couplings and beta functions in 3d and 4d SYM

Developed new software for supersymmetric QCD simulations

Abstract

We present new results from ongoing lattice investigations of supersymmetric Yang--Mills (SYM) theories in three and four space-time dimensions. First considering the maximally supersymmetric 3d theory with $Q = 16$ supercharges, we check that the fermion pfaffian is approximately real and positive, validating phase-quenched RHMC calculations. We then initiate lattice studies of running couplings and non-perturbative $\beta$ functions for $Q = 16$ SYM in both 3d and 4d, using a simple scheme based on Creutz ratios. Finally, we consider 3d SYM with $Q = 8$ supercharges, developing new software as a first step towards supersymmetric QCD.