MODULAR DATA AND VERLINDE FORMULAE FOR FRACTIONAL LEVEL WZW MODELS I

By T. Creutzig, David Ridout. 2012

149 citations recorded by the source corpus.

Abstract The modular properties of fractional level sl ˆ ( 2 ) -theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory have led to the realisation that problems with fractional level models stem from trying to build the theory with an insufficiently rich category of representations. In particular, the appearance of negative fusion coefficients for admissible highest weight representations is now completely understood. Here, the modular story for certain fractional level theories is completed. Modular transformations are derived for the complete set of admissible irreducible representations when the level is k = − 1 2 or k = − 4 3 . The S-matrix data and Verlinde formula are then checked against the known fusion rules with complete agreement. Finally, an infinite set of modular invariant partition functions is constructed in each case.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6831585e2ebb6202b521cde8c252f94dcb1db0c6

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Citations in the corpus

Braided Tensor Categories of Admissible Modules for Affine Lie Algebras (2017, background): “as formal power series of admissible level L(ℓ,0)-modules, a Verlinde formula had been conjectured in [CR1, CR2]. The conjectural fusion rules for ordinary modules are then given in Proposition 15 of [CR2]. 31 Corollary 7.7 Let ℓ = −2+ a b with a,b coprime positive integers and a > 1. The Verlind”
Logarithmic conformal field theory: beyond an introduction (2013, methodology): “t that Verlinde formulae for slb(2) −1/2 and slb(2) −4/3 have been successfully derived using the above formalism suggests that this will generalise to all admissible levels. This will be detailed in [60]. Other afﬁne algebras at admissible levels have not yet received much attention, though slb(3)w”
Fusion categories for affine vertex algebras at admissible levels (2018, background): “So far, David Ridout and I, we conjectured a Verlinde formula for relaxed-highest weight modules of Ll(sl2) at admissible level [30, 31] and indeed the conjecture restricted to ordinary modules is true [12, Cor.”
The worldsheet dual of the symmetric product CFT (2018, background): “In particular, our formula differs from [74].”