Towards a classification of fermionic rational conformal field theories

2023-03-28

 

Titel: Fusion category symmetries of 1+1d bosonic and fermionic topological field theories

Speaker: Kansei Inamura (University of Tokyo)

Time: 9:00 - 11:00, Tue, Mar. 28, 2023

Online: Zoom ID:954 2993 2868  (Passcode: 588289)

 

Abstract:

Generalized symmetries in two-dimensional spacetime are described by the algebraic structure of topological line defects. In particular, when the number of topological lines is finite, their algebraic structure is described by a fusion category or a superfusion category depending on whether the system is bosonic or fermionic. For this reason, finite generalized symmetries in 1+1 dimensions are called fusion category symmetries. In this talk, we will construct 1+1d bosonic and fermionic topological field theories (TQFTs) with fusion category symmetries using the state sum construction of TQFTs and the pullback of fusion category symmetries. These TQFTs can be realized by the ground states of commuting projector Hamiltonians on the lattice. We will also derive the fermionization formula of fusion category symmetries by comparing the symmetries of bosonic TQFTs with those of fermionic TQFTs. Examples include the fermionization of finite group symmetries and Kramers-Wannier-like self-dualities. This talk is based on arXiv:2110.12882 and 2206.13159.

 


 

2023-03-21

 

Titel: Towards a classification of fermionic rational conformal field theories

Speaker: Zhihao Duan (Korea Institute for Advanced Study)

Time: 9:00 - 11:00, Tue, Mar. 21, 2023

Online: Zoom ID:954 2993 2868  (Passcode: 588289)

 

Abstract:

Two-dimensional conformal field theories (CFTs) play an important role in modern theoretical physics. Among them, rational CFTs enjoy particularly nice properties and hence are amenable to a possible classification. In this talk, I will review some recent progress towards classifying Rational CFTs with fermions using the holomorphic modular bootstrap method, which is related to but different from the classification of super modular tensor categories (MTCs). As one of the main results, we successfully bootstrap theories with small number of characters, which already reveal interesting phenomena such as fermionization, SUSY enhancement and the moonshine of sporadic groups. Finally, partly inspired by the congruence property of MTC, we make use of the integrality of characters to improve our classification.

 

【Category and Topological Order Seminar】