Classification of abelian spin Chern-Simons theories

Details Classification of abelian spin Chern-Simons theories Classification of abelian spin Chern-Simons theories

2005-05-25

arxiv.org/abs/hep-th/0505235v1

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, 5 figures, LaTeX

Scientific paper

We derive a simple classification of quantum spin Chern-Simons theories with gauge group T=U(1)^N. While the classical Chern-Simons theories are classified by an integral lattice the quantum theories are classified differently. Two quantum theories are equivalent if they have the same invariants on 3-manifolds with spin structure, or equivalently if they lead to equivalent projective representations of the modular group. We prove the quantum theory is completely determined by three invariants which can be constructed from the data in the classical action. We comment on implications for the classification of fractional quantum Hall fluids.

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