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arXiv · 2007.10562

A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation

Jiaqi Lou·Ce Shen·Chaoyi Chen·Ling-Yan Hung
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Abstract

We study gapped boundaries characterized by "fermionic condensates" in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We also connect these results with topological defects in super modular invariant CFTs. To render our discussion self-contained, we provide a pedagogical review of relevant mathematical results, so that physicists without prior experience in tensor category should be able to pick them up and apply them readily

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Jiaqi Lou, Ce Shen, Chaoyi Chen, Ling-Yan Hung. 2020-07-21. A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation. https://doi.org/10.1007/jhep02(2021)171

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