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

Understand

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.