RG Flows in 2d Chiral Gauge Theories

We study the dynamics of two-dimensional chiral $SU(N)$ gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. A consistent infra-red limit of these theories consists of certain coset CFTs. There is also a free fermion phase which shares the same central charge and 't Hooft anomalies but does not coincide with the coset models. We show that these two theories sit on a conformal manifold of infra-red theories and are related by a current-current deformation. We further consider extensions of these theories by adding Dirac fermions and comment on possible RG flows.