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

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

2011-06-23

arxiv.org/abs/1106.4641v3

New J. Phys. 14, 013060 (2012)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

version to appear in New Journal of Physics

Scientific paper

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.

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