Chiral edge modes from lattice Chern-Simons theory

Abstract

It is shown that a level $k$ Abelian lattice Chern-Simons theory with continuum time and a spatial square lattice, which is a topological field theory on the latticized plane and torus, when quantized on a spatial cylinder reduces to chiral edge excitations, exactly localized on the two boundaries and carrying two commuting lattice versions of the level-$k$ $U(1)$ Kac-Moody algebra of opposite chirality. The algebras are represented on a Fock space in the noncompact theory and by a finite Weyl algebra in the compact one. We also observe that the theory has a natural framing of Wilson loops which exhibits the correct framing anomaly.