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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Lou, J., Shen, C., Chen, C. et al. A (dummy’s) guide to working with gapped boundaries via (fermion) condensation. J. High Energ. Phys. 2021, 171 (2021). https://doi.org/10.1007/JHEP02(2021)171
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DOI: https://doi.org/10.1007/JHEP02(2021)171