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

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

52 pages main text and 22 pages appendix, mathematica code for computing 6j symbols of condensed phase included; correct some typos and equations; correct some typos and rearrange the position of some figures