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 $\alpha = N_L / N_T \leq 4$ 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 $T_c \propto \alpha^3$.