Nonperturbative phase diagram of two-dimensional ${\cal N} = (2, 2)$ super-Yang--Mills

We consider two-dimensional ${\cal N} = (2, 2)$ Yang--Mills theory with gauge group SU($N$) in Euclidean signature compactified on a torus with thermal fermion boundary conditions imposed on one cycle. We perform non-perturbative lattice analyses of this theory for large $12 \leq N \leq 20$. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional ${\cal N} = (8, 8)$ Yang--Mills theory, which has a well-defined gravity dual. We perform lattice field theory calculations to determine the phase diagram, observing a spatial deconfinement transition similar to the maximally supersymmetric case. However, the transition does not continue to low temperature, implying the absence of a topology-changing transition between black hole geometries in any holographic dual for this four-supercharge theory.