Fermionic CFTs and classifying algebras

Abstract

We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from the change of spin structure in different limits. We define fermionic classifying algebras for boundaries, defects, and interfaces, which allow one to read off the elementary boundary conditions, etc. As examples, we define fermionic extensions of Virasoro minimal models and give explicit solutions for the spectrum and bulk structure constants. We show how the Aand D-type fermionic Virasoro minimal models are related by a parity-shift operation which we define in general. We study the boundaries, defects, and interfaces in several examples, in particular in the fermionic Ising model, i.e. the free fermion, in the fermionic tri-critical Ising model, i.e. the first unitary N = 1 superconformal minimal model, and in the supersymmetric Lee-Yang model, of which there are two distinct versions that are related by parity-shift.

Symmetries and strings of adjoint QCD2

“…In most of this paper we have worked with the topological lines in the bosonized theory. This is to avoid technical complications, and also because of lack of literature completing the theory of lines in a fermionic theory, though there are remarkable papers [93,95,[162][163][164][165][166][167][168][169]. 54 Based on this literature, here we give a brief outlook of the topological lines in fermionic theories, and give an explicit example of topological lines in the fermionic SU(3) adjoint QCD.…”

The non-rational limit of D-series minimal models

“…Our approach could be generalized to other families of exactly solvable CFTs whose central charges are dense in a line. This includes minimal models for extended symmetry algebras, and fermionic minimal models [15]. The limit of the fermionic minimal model's nondiagonal sector is of the type of Eq.…”

Two more fermionic minimal models

“…For the unitary minimal models, it is (literally) a textbook result (see 10.7 of [7]) that the Z 2 symmetry of any of the A-type theories can be gauged to produce the D-type theory and vice-versa. 2 3 Fermionic minimal models…”