Alexei Davydov

Invertible defects and isomorphisms of rational CFTs

Given two two-dimensional conformal field theories, a domain wall —or defect line— between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and is compatible with the operator product expansion. We show that for rational CFTs there is a one-to-one correspondence between invertible topological defects and conformal isomorphisms if both preserve the rational symmetry. This correspondence is compatible with composition.

Holomorphic symplectic fermions

Let V be the even part of the vertex operator super-algebra of r pairs of symplectic fermions. Up to two conjectures, we show that V admits a unique holomorphic extension if r is a multiple of 8, and no holomorphic extension otherwise. This is implied by two results obtained in this paper: (1) If r is a multiple of 8, one possible holomorphic extension is given by the lattice vertex operator algebra for the even self dual lattice

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

D_{r}^+

The Picard crossed module of a braided tensor category

Dr+ with shifted stress tensor. (2) We classify Lagrangian algebras in

Z/2Z-extensions of Hopf algebra module categories by their base categories

\mathcal {S}\mathcal {F}(\mathfrak {h})

A braided monoidal category for symplectic fermions

SF(h), a ribbon category associated to symplectic fermions. The classification of holomorphic extensions of V follows from (1) and (2) if one assumes that