Modular data and Verlinde formulae for fractional level WZW models II

Creutzig T, Ridout D (2013)

Publication Type: Journal article

Publication year: 2013

Journal

Nuclear Physics B Elsevier

Book Volume: 875

Pages Range: 423-458

Journal Issue: 2

DOI: 10.1016/j.nuclphysb.2013.07.008

Abstract

This article gives a complete account of the modular properties and Verlinde formula for conformal field theories based on the affine Kac-Moody algebra sl̂(2) at an arbitrary admissible level k. Starting from spectral flow and the structure theory of relaxed highest weight modules, characters are computed and modular transformations are derived for every irreducible admissible module. The culmination is the application of a continuous version of the Verlinde formula to deduce non-negative integer structure coefficients which are identified with Grothendieck fusion coefficients. The Grothendieck fusion rules are determined explicitly. These rules reproduce the well-known "fusion rules" of Koh and Sorba, negative coefficients included, upon quotienting the Grothendieck fusion ring by a certain ideal. © 2013 Elsevier B.V.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

University of Alberta CA Canada (CA) Australian National University (ANU) AU Australia (AU)

How to cite

APA:

Creutzig, T., & Ridout, D. (2013). Modular data and Verlinde formulae for fractional level WZW models II. Nuclear Physics B, 875(2), 423-458. https://doi.org/10.1016/j.nuclphysb.2013.07.008

MLA:

Creutzig, Thomas, and David Ridout. "Modular data and Verlinde formulae for fractional level WZW models II." Nuclear Physics B 875.2 (2013): 423-458.

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