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

Journal of High Energy Physics

Jiaqi Lou¹  Ling-Yan Hung¹  Ce Shen¹  Chaoyi Chen¹ 

[1] State Key Laboratory of Surface Physics, Fudan University, 2005 Songhu Road, 200433, Shanghai, China;Shanghai Qi Zhi Institute, 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, 200232, Shanghai, China;Department of Physics and Center for Field Theory and Particle Physics, Fudan University, 2005 Songhu Road, 200433, Shanghai, China;Institute for Nanoelectronic devices and Quantum computing, Fudan University, 2005 Songhu Road, 200433, Shanghai, China;

关键词: Anyons;    Topological States of Matter;    Chern-Simons Theories;    Conformal Field Theory;   

DOI  :  10.1007/JHEP02(2021)171

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY