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

We study 2d SU(N) QCD with an adjoint Dirac fermion. Assuming that the IR limit of the massless theory is captured by a WZW coset CFT, we show that this CFT can be decomposed into a sum of distinct CFTs, each representing a superselection sector (universe) of the gauge theory corresponding to different flux tube sectors. The CFTs describing each universe are related by non-invertible topological lines that exhibit a mixed anomaly with the ${\mathbb{Z}}_N^{\left(1\right)}$ \( {\mathbb{Z}}_N^{(1)} \) 1-form symmetry. These symmetries exists along the entire RG flow thereby implying deconfinement of the massless theory. We begin by outlining the general features of the model for arbitrary N and then provide a detailed analysis for N = 2 and N = 3. In these specific cases, we explicitly determine the IR partition function, identify the symmetries, and explore relevant deformations. Based on these findings and in alignment with various previous studies, we propose a phase diagram for the massive SU(2) gauge theory and calculate its confining string tension.