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 𝛽 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.

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 𝛽 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.

We present ongoing investigations of maximally supersymmetric Yang-Mills (𝑄 = 16 SYM) theory in three space-time dimensions. At low temperatures and large 𝑁 this theory is related to black branes in higher-dimensional quantum gravity. Building on previous work that focused on the homogeneous 'D2' phase of the theory, we are now exploring phase transitions between this D2 phase and the localized 'D0' phase.