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

A bstract 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 $$ {\mathbb{Z}}_N^{(1)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℤ</mml:mi> <mml:mi>N</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> 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.