A (dummy’s) guide to working with gapped boundaries via (fermion) condensation

Abstract

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.

Keywords

• Anyons
• Topological States of Matter
• Chern-Simons Theories
• Conformal Field Theory