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

Abstract

We consider two-dimensional $\mathcal{N}=(2,2)$ 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 $12\le N\le 20$. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional $\mathcal{N}=(8,8)$ 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.

v2: Added references, no change in results. Version consistent with the journal version. Data release at http://doi.org/10.5281/zenodo.10083864, 15 pages, 5 figures