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I know this conclusion in topological order for a while: "the topological degeneracy on torus is equal to the number of quasiparticles types."

But can anyone give a physical argument that supports this conclusion? Especially in Non-Abelian case.

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My answer is based on string-net models. Consider a 2D gapped topological system on torus. Mathematically, ground states of the system are characterized by representations of quantum double of the input group/quantum group. The quasiparticles carry quantum numbers also classified by representations of the quantum double. Described by the same mathematical object, their numbers are of course the same. For a physical picture, every ground state of the system can be labeled by one type of excitation running through the torus.

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