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

Understand

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 the Symanzik's separability condition.

• In both cases on the edges we obtain Ka\v{c}--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.