Torus ground-state degeneracy of an Abelian Chern--Simons theory

An Abelian K-matrix Chern--Simons theory has

∣ det K ∣

topologically distinct ground states on a torus.

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- Wilson-loop algebra of an Abelian Chern--Simons theory Torus ground-state degeneracy of an Abelian Chern--Simons theory

Wilson-loop algebra of an Abelian Chern--Simons theory

Quasiparticle transport around the two fundamental cycles of a torus gives loop operators obeying

T_{x} (q^{'}) T_{y} (q) = e^{2 πi q^{' T} K^{- 1} q} T_{y} (q) T_{x} (q^{'}) .

The induced pairing on

Z^{n} / K Z^{n}

is nondegenerate, so this algebra has a representation of dimension at least

∣ det K ∣

.

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