Fusion matrices, generalized Verlinde formulas and partition functions in WLM(1,p)

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 10, 2010, Pages

  Rasmussen, Jørgen ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77149121385     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/10/105201     Document Type: Article

References (38)

1. Verlinde E 1988 Fusion rules and modular transformations in 2D conformal field theory Nucl. Phys. B 300 360-76
2. Francesco P Di, Mathieu P and Sénéchal D 1996 Conformal Field Theory (Berlin: Springer)
3. Pearce P A and Rasmussen J On the classification of logarithmic minimal models (in preparation)
4. Pearce P A, Rasmussen J and Ruelle P 2010 Grothendieck ring and Verlinde formula for the -extended logarithmic minimal model J. Phys. A: Math. Theor. 43 045211 (arXiv:0907.0134 [hep-th])
5. Pearce P A, Rasmussen J and Zuber J-B 2006 Logarithmic minimal models J. Stat. Mech. P11017 (arXiv:hep-th/0607232)
6. Pearce P A, Rasmussen J and Ruelle P 2008 Integrable boundary conditions and -extended fusion in the logarithmic minimal models J. Phys. A: Math. Theor. 41 295201 (arXiv:0803.0785 [hep-th])
7. Gaberdiel M R and Kausch H G 1996 A rational logarithmic conformal field theory Phys. Lett. B 386 131-7 (arXiv:hep-th/9606050)
8. Eberle H and Flohr M 2006 Virasoro representations and fusion for general augmented minimal models J. Phys. A: Math. Gen. 39 15245-86 (arXiv:hep-th/0604097)
9. Gaberdiel M R and Runkel I 2008 From boundary to bulk in logarithmic CFT J. Phys. A: Math. Theor. 41 075402 (arXiv:0707.0388 [hep-th])
10. Rasmussen J 2009 Polynomial fusion rings of -extended logarithmic minimal models J. Math. Phys. 50 043512 (arXiv:0812.1070 [hep-th])
11. Fuchs J, Hwang S, Semikhatov A M and Tipunin I Yu 2004 Nonsemisimple fusion algebras and the Verlinde formula Commun. Math. Phys. 247 713-42 (arXiv:hep-th/0306274)
12. p, 1 logarithmic conformal field theories arXiv:0705.0545 [math-ph]
13. Gainutdinov A M and Tipunin I Yu 2009 Radford, Drinfeld, and Cardy boundary states in (1, p) logarithmic conformal field models J. Phys. A: Math. Theor. 42 315207 (arXiv:0711.3430 [hep-th])
14. Rasmussen J and Pearce P A 2008 -extended fusion algebra of critical percolation J. Phys. A: Math. Theor. 41 295208 (arXiv:0804.4335 [hep-th])
15. Rasmussen J 2009 -extended logarithmic minimal models Nucl. Phys. B 807 495-533 (arXiv:0805.2991 [hep-th])
16. Gaberdiel M R, Runkel I and Wood S 2009 Fusion rules and boundary conditions in the c = 0 triplet model J. Phys. A: Math. Theor. 42 325403 (arXiv:0905.0916 [hep-th])
17. Rasmussen J 2010 Fusion of irreducible modules in J. Phys. A: Math. Theor. 43 045210 (arXiv:0906.5414 [hep-th])
18. Wood S 2010 Fusion rules of the triplet models J. Phys. A: Math. Theor. 43 045212 (arXiv:0907.4421 [hep-th])
19. Gepner D 1991 Fusion rings and geometry Commun. Math. Phys. 141 381-411
20. Mason J C and Handscomb D C 2003 Chebyshev Polynomials (Boca Raton, FL: Chapman & Hall/CRC)
21. Behrend R E, Pearce P A, Petkova V B and Zuber J-B 1998 On the classification of bulk and boundary conformal field theories Phys. Lett. B 444 163-6 (arXiv:hep-th/9809097)
22. Behrend R E, Pearce P A, Petkova V B and Zuber J-B 2000 Boundary conditions in rational conformal field theories Nucl. Phys. B 579 707-73 (arXiv:hep-th/9908036)
23. Ocneanu A 1999 Paths on Coxeter diagrams: from platonic solids and singularities to minimal models and subfactors, notes taken by S. Goto Fields Institute Monographs ed R Bhat et al (Providence, RI: American Mathematical Society)
24. Ocneanu A 2002 The classification of subgroups of quantum SU(N) Quantum Symmetries in Theoretical Physics and Mathematics ed R Coquereaux, A García and R Trinchero (Providence, RI: American Mathematical Society)
25. Ocneanu A 2000 Contemp. Math. 294 133-59
26. Petkova V B and Zuber J-B 2001 Generalized twisted partition functions Phys. Lett. B 504 157-64 (arXiv:hep-th/0011021)
27. Petkova V B and Zuber J-B 2001 The many faces of Ocneanu cells Nucl. Phys. B 603 449-96 (arXiv:hep-th/0101151)
28. n coset models on the torus Nucl. Phys. B 300 559-87
29. Francesco P Di and Zuber J-B 1990 SU(N) lattice integrable models associated with graphs Nucl. Phys. B 338 602-46
30. Francesco P Di 1992 Integrable lattice models, graphs and modular invariant conformal field theories Int. J. Mod. Phys. A 7 407
31. Petkova V B and Zuber J-B 1996 From CFT to graphs Nucl. Phys. B 463 161-93 (arXiv:hep-th/9510175)
32. Flohr M 1996 On modular invariant partition functions of conformal field theories with logarithmic operators Int. J. Mod. Phys. A 11 4147-72 (arXiv:hep-th/9509166)
33. Flohr M 1997 On fusion rules in logarithmic conformal field theories Int. J. Mod. Phys. A 12 1943-58 (arXiv:hep-th/9605151)
34. Flohr M and Gaberdiel M R 2006 Logarithmic torus amplitudes J. Phys. A: Math. Gen. 39 1955-68 (arXiv:hep-th/0509075)
35. Feigin B L, Gainutdinov A M, Semikhatov A M and Tipunin I Y 2006 Logarithmic extensions of minimal models: characters and modular transformations Nucl. Phys. B 757 303-43 (arXiv:hep-th/0606196)
36. Penrose R 1955 A generalized inverse for matrices Proc. Cambridge Philos. Soc. 51 406-13
37. Ben Israel A and Greville T N E 2003 Generalized Inverses: Theory and Applications (Berlin: Springer)
38. Rasmussen J 2009 Graph fusion algebras of arXiv:0911.3229