Maximally supersymmetric Yang--Mills in three dimensions

We present the latest results from our ongoing lattice field theory investigations of maximally supersymmetric Yang–Mills theory in three space-time dimensions, focusing on its non-perturbative phase diagram. Exploiting a lattice formulation that preserves a subset of the supersymmetry algebra at non-zero lattice spacing, we study the ‘spatial deconfinement’ phase transition that holography relates to the transition between localized and homogeneous black branes in the dual quantum gravity. Fixing $N_L^2\times 8$ lattice volumes and N=8 colors in the SU(N) gauge group, we consider four aspect ratios $\alpha =N_L\mathrm{/}{N}_T\le 4$ corresponding to $N_L=16$, $20$, $24$ and $32$. The transition temperatures we determine are in good agreement with the low-temperature, large-N holographic expectation $T_c\propto {\alpha }^3$.