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Fermionic CFTs and classifying algebras

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Ingo Runkel, Gerard Watts

Original languageEnglish
Article number25
Number of pages44
JournalJournal of High Energy Physics
Issue number6
Publication statusPublished - 3 Jun 2020


King's Authors


We study fermionic conformal held 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 o 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 A- and 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 rst 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.

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