Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions
Jurgen Fuchs, Ingo Runkel, Christoph Schweigert
Abstract
A Morita class of symmetric special Frobenius algebras A in the modular tensor category of a chiral CFT determines a full CFT on oriented world sheets. For unoriented world sheets, A must in addition possess a reversion, i.e. an isomorphism from Aopp to A squaring to the twist. Any two reversions of an algebra A differ by an element of the group Aut(A) of algebra automorphisms of A. We establish a group homomorphism from Aut(A) to the Picard group of the bimodule category CAA, with kernel consisting of the inner automorphisms, and we refine Morita equivalence to an equivalence relation between algebras with reversion.
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