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

Abstract

Abstract 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 ℤ N 1 $$ {\mathbb{Z}}_N^{(1)} $$ 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.

Keywords

• Confinement
• Conformal and W Symmetry
• Field Theories in Lower Dimensions
• Global Symmetries