I keep hearing that a gauged 2D topological superconductor with preserved time-reversal symmetry that belongs to the DIII class is equivalent to the Z_2 gauge theory (Z_2 topological order with excitations being those of the toric code). Can anyone help me understand that statement and refer to relevant literature? Thank you.

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    $\begingroup$ The distinction comes from whether you consider the electromagnetic field to be dynamical or just a fixed background. See physics.stackexchange.com/questions/71351/… $\endgroup$ – Seth Whitsitt Nov 9 '19 at 17:00
  • $\begingroup$ Are there any papers particularly dealing with gauged topological superconductors and proving the equivalence with the Z2 gauge theory? Thanks! $\endgroup$ – danport Nov 11 '19 at 15:30
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    $\begingroup$ The closest I can think of is the paper linked in the above question, arxiv.org/abs/cond-mat/0404327 which is pretty exhaustive. They explicitly show how superconductors and Z2 lattice gauge theories lead to the same topological QFT at low energies. They don't bother with discussing whether the superconductor has additional ("symmetry-enriched") orders like what you are discussing, but the point is that superconductors always have Z2 topological order. $\endgroup$ – Seth Whitsitt Nov 12 '19 at 2:37

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