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      Fusion rules for permutation extensions of modular tensor categories

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          Abstract

          We give a construction and algorithmic description of the fusion ring of permutation extensions of an arbitrary modular tensor category using a combinatorial approach inspired by the physics of anyons and symmetry defects in bosonic topological phases of matter. The definition is illustrated with examples, namely bilayer symmetry defects and \(S_3\)-extensions of small modular tensor categories like the Ising and Fibonacci theories. An implementation of the fusion algorithm is provided in the form of a Mathematica package. We introduce the notions of confinement and deconfinement of anyons and defects, respectively, which develop the tools to generalize our approach to more general fusion rings of \(G\)-crossed extensions.

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          Tensor Categories

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            Twist defects and projective non-Abelian braiding statistics

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              Topological Quantum Computation

               Zhenghan Wang (2010)
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                Author and article information

                Journal
                06 September 2019
                Article
                1909.03003

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                18
                math.QA cond-mat.str-el math-ph math.MP quant-ph

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