Symmetries, universes and phases of QCD2 with an adjoint Dirac fermion

Abstract

We study 2d SU(N) QCD with an adjoint Dirac fermion. Assuming that the IRlimit of the massless theory is captured by a WZW coset CFT, we show that this CFTcan be decomposed into a sum of distinct CFTs, each representing a superselectionsector (universe) of the gauge theory corresponding to different flux tube sectors. TheCFTs describing each universe are related by non-invertible topological lines that exhibit a mixed anomaly with the Z^(1)_N 1-form symmetry. These symmetries exists alongthe entire RG flow thereby implying deconfinement of the massless theory. We begin byoutlining the general features of the model for arbitrary N and then provide a detailedanalysis for N = 2 and N = 3. In these specific cases, we explicitly determine the IRpartition function, identify the symmetries, and explore relevant deformations. Basedon these findings and in alignment with various previous studies, we propose a phasediagram for the massive SU(2) gauge theory and calculate its confining string tension.