The Verlinde formula in logarithmic CFT
Published in Proceedings for the 30th ICGTMP (Ghent, 2014), 2014
A review that refines, through simple examples, the standard module formalism for modular transformations and Verlinde formulae in logarithmic conformal field theory. It also explains how fusion rules behave under simple current extensions, reaching logarithmic theories not covered directly by the standard module formalism.
Abstract
In rational conformal field theory, the Verlinde formula computes the fusion coefficients from the modular S-transformations of the characters of the chiral algebra’s representations. Generalising this formula to logarithmic models has proven rather difficult for a variety of reasons. Here, a recently proposed formalism (arXiv:1303.0847 [hep-th]) for the modular properties of certain classes of logarithmic theories is reviewed, and refined, using simple examples. A formalism addressing fusion rules in simple current extensions is also reviewed as a means to tackle logarithmic theories to which the proposed modular formalism does not directly apply.
Recommended citation: D. Ridout and S. Wood, J. Phys.: Conf. Ser. 597 012065 (2015)
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