Why are topological phases described by modular tensor categories?

Question

After some reading, I have an inuitive idea what topological phases of matter are. But where is the connection to modular tensor categories? Is there fundamental literature where this is covered?

Edit: A topological phase is characterized by a TQFT as low-energy effective theory. Furthermore, every modular tensor category leads to a TQFT, as shown by Turaev. However, according to Wang, "Topological Quantum Computation" (CBMS, Vol. 112, 2010), the converse is only a conjecture. Is it already proven that a strict fusion category of a TQFT can be extended uniquely to a modular tensor category compatible with the TQFT? Even if it is: Is there a more illustrative explanation why modular tensor categories are studied as mathematical models for topological phases?

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user mathphys-kolaka

Comments

Have you read the relevant This Week's Finds?

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user AHusain

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@AHusain What do you mean? Please add a link.

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user mathphys-kolaka

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John Baez Week 137

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user AHusain

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this this one physics.stackexchange.com/q/5029/12961

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user john mangual

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@AHusain : Thanks, this gives a bit of context, but I'm afraid this does not completely answer my question. There still seems to be a "missing link" between the physicist's and the mathematician's viewpoint.

This post imported from StackExchange Physics at 2016-08-12 08:54 (UTC), posted by SE-user mathphys-kolaka