The motivation for this question comes from observing that the toric code model has the properties of a TQFT (robust ground state degeneracy) and of a $\mathbb Z_2$ gauge theory (local spin flips don't change the Hamiltonian). The question is, is there any general relationship between TQFTs and gauge theories: does one imply the other, or can they be related in some limit, say at zero temperature?
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