Geodesic
A~generalization of the~Verlinde formula in~logarithmic conformal field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 194-206

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We propose a generalized Verlinde formula associated with $(1,p)$ logarithmic models of two-dimensional conformal field theories, which have applications in statistical physics problems such as the sand-pile model and phase transitions in polymers. This formula gives the integer structure constants in the whole $(3p{-}1)$-dimensional space of vacuum torus amplitudes in which the fusion algebra is a $2p$-dimensional subalgebra.
Keywords: conformal field theory, logarithmic model, nonsemisimple fusion algebra, Verlinde formula. 
@article{TMF_2009_159_2_a1,
     author = {A. M. Gainutdinov},
     title = {A~generalization of {the~Verlinde} formula in~logarithmic conformal field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {194--206},
     publisher = {mathdoc},
     volume = {159},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a1/}
}
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A. M. Gainutdinov. A~generalization of the~Verlinde formula in~logarithmic conformal field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 194-206. http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a1/