CMSA Quantum Matter in Mathematics and Physics: Gapped Boundaries, Junctions via (fermionic) anyon condensation
Janet Ling Yan Hung - Fudan University
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 will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.