From non-semisimple Hopf algebras to correlation functions for logarithmic CFT

Abstract

We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For any ribbon Hopf algebra automorphism omega of H we present a candidate for the space of bulk fields and endow it with a natural structure of a commutative symmetric Frobenius algebra. We derive an expression for the corresponding bulk partition functions as bilinear combinations of irreducible characters; as a crucial ingredient this involves the Cartan matrix of the category. We also show how for any candidate bulk state space of the type we consider, correlation functions of bulk fields for closed oriented world sheets of any genus can be constructed that are invariant under the natural action of the relevant mapping class group.

41 pages, several figures. version 2: typos corrected, bibliography updated, introduction extended, a few minor clarifications added

References in corpus (6)

• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• From boundary to bulk in logarithmic CFT
• Logarithmic torus amplitudes
• Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models
• RCFT with defects: Factorization and fundamental world sheets
• The Cardy-Cartan modular invariant

Cited by in corpus (9)

• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• Symplectic fermions and a quasi-Hopf algebra structure on ${\bar{U}}_{i}sl(2)$
• SL(2,Z)-action for ribbon quasi-Hopf algebras
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Renormalized Hennings Invariants and 2+1-TQFTs
• The logarithmic Cardy case: Boundary states and annuli
• The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
• A non-semisimple non-invertible symmetry