RG flows in 2d QCD

Abstract

2d QCD, Yang-Mills theory with gauge group G and massless quarks in representations (Rℓ, Rr) of G, flows in the infrared to a CFT or a TQFT depending on whether spectrum is gapless or gapped. We identify the infrared effective theory and construct the explicit RG flow map between the QCD operators in the UV and the IR, in particular identifying which operators create massive excitations and decouple in the IR, and those that create massless excitations or vacua and remain as nontrivial IR operators. We determine the exact scaling dimensions of the QCD operators that remain in the IR, which generically acquire large anomalous dimensions. We also study QCD deformed by various operators in the ultraviolet (such as mass terms or four-fermi interactions), and determine the theory that emerges at low energies. We conjecture and provide some evidence for QCD deformed by various operators developing a nonperturbative fermion condensate that dynamically breaks the gauge symmetry G, thus explicitly realizing an old idea known as “tumbling” in an exactly soluble setting.