Geodesic
A generalization of the Verlinde formula in logarithmic conformal field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 194-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {A~generalization of {the~Verlinde} formula in~logarithmic conformal field theory},
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}
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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/

[1] M. R. Gaberdiel, H. G. Kausch, Phys. Lett. B, 386:1–4 (1996), 131–137 ; arXiv: hep-th/9606050 | DOI | MR

[2] P. A. Pearce, J. Rasmussen, J.-B. Zuber, J. Stat. Mech. Theory Exp., 2006:11 (2006), 11017 ; arXiv: hep-th/0607232 | DOI | MR

[3] B. L. Feigin, A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin, Nucl. Phys. B, 757:3 (2006), 303–343 ; arXiv: hep-th/0606196 | DOI | MR | Zbl

[4] A. M. Semikhatov, TMF, 153:3 (2007), 291–346 ; arXiv: hep-th/0701279 | DOI | MR | Zbl

[5] H. Eberle, M. Flohr, J. Phys. A, 39:49 (2006), 15245–15286 ; arXiv:hep-th/0604097 | DOI | MR | Zbl

[6] G. Piroux, P. Ruelle, J. Stat. Mech. Theory Exp., 2004:10 (2004), 10005 ; arXiv: hep-th/0407143 | DOI | MR | Zbl

[7] J. Cardy, J. Phys. A, 25:4 (1992), L201–L206 ; arXiv: hep-th/9111026 | DOI | MR | Zbl

[8] G. M. T. Watts, J. Phys. A, 29:14 (1996), L363–L368 ; arXiv: cond-mat/9603167 | DOI | MR | Zbl

[9] D. Adamović, A. Milas, Adv. Math., 217:6 (2008), 2664–2699 ; arXiv: 0707.1857 | DOI | MR | Zbl

[10] M. R. Gaberdiel, H. G. Kausch, Nucl. Phys. B, 477:1 (1996), 293–318 ; arXiv: hep-th/9604026 | DOI | MR

[11] H. G. Kausch, Phys. Lett. B, 259:4 (1991), 448–455 | DOI | MR

[12] J. Fuchs, S. Hwang, A. M. Semikhatov, I. Yu. Tipunin, Comm. Math. Phys., 247:3 (2004), 713–742 ; arXiv: hep-th/0306274 | DOI | MR | Zbl

[13] E. P. Verlinde, Nucl. Phys. B, 300:3 (1988), 360–376 | DOI | MR | Zbl

[14] B. L. Feigin, A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin, Comm. Math. Phys., 265:1 (2006), 47–93 ; arXiv: hep-th/0504093 | DOI | MR | Zbl

[15] B. L. Feigin, A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin, J. Math. Phys., 48:3 (2007), 032303 ; arXiv: math.QA/0606506 | DOI | MR | Zbl

[16] A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin, B. L. Feigin, TMF, 148:3 (2006), 398–427 ; arXiv: math.QA/0512621 | DOI | MR | Zbl

[17] A. M. Semikhatov, TMF, 154:3 (2008), 510–535 ; arXiv: 0705.4267 | DOI | MR | Zbl

[18] A. M. Gainutdinov, I. Yu. Tipunin, Radford, Drinfeld, and Cardy boundary states in $(1,p)$ logarithmic conformal field models, arXiv: 0711.3430 | MR

[19] M. A. I. Flohr, Internat. J. Modern Phys. A, 11:22 (1996), 4147–4172 ; arXiv: hep-th/9509166 | DOI | MR | Zbl

[20] G. Moore, N. Seiberg, Phys. Lett. B, 212:4 (1988), 451–460 | DOI | MR

[21] G. Moore, N. Seiberg, Nucl. Phys. B, 313:1 (1989), 16–40 | DOI | MR

[22] V. G. Drinfeld, Algebra i analiz, 1:2 (1989), 30–46 | MR | Zbl

[23] D. E. Radford, J. Algebra, 163:3 (1994), 583–622 | DOI | MR | Zbl

[24] M. A. I. Flohr, H. Knuth, On Verlinde-like formulas in $c_{p,1}$ logarithmic conformal field theories, arXiv: 0705.0545

[25] M. R. Gaberdiel, I. Runkel, J. Phys. A, 41:7 (2008), 075402 ; arXiv: 0707.0388 | DOI | MR | Zbl

[26] M. Flohr, M. R. Gaberdiel, J. Phys. A, 39:8 (2006), 1955–1967 ; arXiv: hep-th/0509075 | DOI | MR | Zbl | MR