  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.
