The Verlinde formula in logarithmic CFT

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.Comment: 12 pages, proceedings article for the 30th ICGTMP (Ghent, 2014); v2 fixed an erroneous statement pointed out by Antun Milas; v3 made a few minor clarifications to discussion and added a couple of ref