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arXiv · 1909.03003

Fusion rules for permutation extensions of modular tensor categories

Colleen Delaney
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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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Colleen Delaney. 2019-09-06. Fusion rules for permutation extensions of modular tensor categories. https://arxiv.org/abs/1909.03003

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