  Using the duality between seemingly different (2+1)d conformal field theories
(CFT) proposed recently, we study a series of (2+1)d stable self-dual
interacting CFTs. These CFTs can be realized (for instance) on the boundary of
the (3+1)d bosonic topological insulator protected by U(1) and time-reversal
symmetry, and they remain stable as long as these symmetries are preserved.
When realized as a boundary system, these CFTs can be driven into anomalous
fractional quantum Hall states once time-reversal is broken. We demonstrate
that the newly proposed dualities allow us to study these CFTs quantitatively
through a controlled calculation, without relying on a large flavor number of
matter fields.
