Non-Abelian BF theory for 2+1 dimensional topological states of matter

We present a field theoretical analysis of the 2 + 1 dimensional BF model with boundary in the Abelian and the non-Abelian case based on Symanzik's separability condition. Our aim is to characterize the low-energy properties of time reversal invariant topological insulators. In both cases, on the edges, we obtain Kac-Moody algebras with opposite chiralities reflecting the time reversal invariance of the theory. While the Abelian case presents an apparent arbitrariness in the value of the central charge, the physics on the boundary of the non-Abelian theory is completely determined by time reversal and gauge symmetry. The discussion of the non-Abelian BF model shows that time reversal symmetry on the boundary implies the existence of counter-propagating chiral currents.