Abstract
We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool is the theory of permutation equivariant modular functors developed by Barmeier et al. in math.CT/0812.0986 and math.QA/1004.1825.
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