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In this answer, it is said that gauging the symmetry which protects a symmetry-protected topological (trivial) phase gives something "morally very similar" to a phase with a topological order. What are the properties which the resultant phase generically does and does not share with the topologically ordered phase?

Any reference which discusses the issue systematically would be appreciated.

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  • $\begingroup$ SPT is an acronym that most readers will not know. You should write it out. $\endgroup$ – G. Smith Dec 20 '19 at 18:09
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I think that when we gauge a global symmetry of an SPT phase, we get an honest TO phase and not just a moral one. The gauge fluxes act as quasiparticles of the TO phase, and the quasiparticle content and statistics gives us invariants of the TO and hence of the "parent" SPT phase. There are many details of this that I am not expert in though, and I'd be happy to be corrected.

Here are some references:

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  • $\begingroup$ Thank you. Let's wait and see if others have something to add. Meanwhile, do you also think that given a TO with an emergent gauge theory you can always associate to it a consistent theory of SPT phase with the corresponding global symmetry? $\endgroup$ – AMA Dec 21 '19 at 0:46

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