Modular differential equations and null vectors

Journal of High Energy Physics

Volumn 2008, Issue 9, 2008, Pages

  Gaberdiel, Matthias R ^a   Keller, Christoph A ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

AdS CFT correspondence; Conformal field models in string theory

Indexed keywords

EID: 58149316411     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/09/079     Document Type: Article

References (33)

1. T. Eguchi and H. Ooguri, Conformal and current algebras on general Riemann surface 1987 Nucl. Phys. B 282 308
2. G. Anderson and G.W. Moore, Rationality in conformal field theory 1988 Comm. Math. Phys. 117 441
3. S.D. Mathur, S. Mukhi and A. Sen, On the classification of rational conformal field theories 1988 Phys. Lett. B 213 303
4. S.D. Mathur, S. Mukhi and A. Sen, Reconstruction of conformal field theories from modular geometry on the torus 1989 Nucl. Phys. B 318 483
5. W. Eholzer, On the classification of modular fusion algebras 1995 1995 Comm. Math. Phys. 172 623 [hep-th/9408160]
6. W. Eholzer, Fusion algebras and characters of rational conformal field theories Ph.D. thesis, Bonn Germany BONN-IR-95-10 [hep-th/9502160]
7. W. Eholzer and N.-P. Skoruppa, Modular invariance and uniqueness of conformal characters 1995 Comm. Math. Phys. 174 117 [hep-th/9407074]
8. W. Eholzer and N.-P. Skoruppa, Conformal characters and theta series 1995 Lett. Math. Phys. 35 197 [hep-th/9410077]
9. M. Flohr and M.R. Gaberdiel, Logarithmic torus amplitudes 2006 J. Phys. A: Math. Gen. 39 1955 [hep-th/0509075]
10. P. Bantay and T. Gannon, Vector-valued modular functions for the modular group and the hypergeometric equation [0705.2467]
11. Y. Zhu, Vertex operator algebras, elliptic functions and modular forms Caltech preprint (1990), 1996 J. Am. Math. Soc. 9 237
12. W. Nahm, A proof of modular invariance 1991 Int. J. Mod. Phys. A 6 2837
13. M.R. Gaberdiel, Constraints on extremal self-dual CFTs 2007 J. High Energy Phys. JHEP11(2007)087 [0707.4073]
14. E. Witten, Three-dimensional gravity revisited [0706.3359]
15. I. Frenkel, J. Lepowsky and A. Meurman, Vertex operator algebras and the Monster (Academic Press), (1988)
16. R.E. Borcherds, Vertex operator algebras, Kac-Moody algebras and the Monster 1986 Proc. Natl. Acad. Sci. U.S.A. 83 3026
17. T. Gannon, Moonshine beyond the monster: the bridge connecting algebra, modular forms and physics (Cambridge University Press, Cambridge) U.K. (2006)
18. G. Höhn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster Ph.D. thesis (Bonn 1995), 1996 Bonner Math. Schriften 286 1 [0706.0236]
19. D. Gaiotto and X. Yin, Genus two partition functions of extremal conformal field theories 2007 J. High Energy Phys. JHEP08(2007)029 [0707.3437]
20. 3 partition functions reconstructed 2007 J. High Energy Phys. JHEP10(2007)103 [0707.1159]
21. X. Yin, Partition functions of three-dimensional pure gravity [0710.2129]
22. X. Yin, On non-handlebody instantons in 3D gravity [0711.2803]
23. A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions [0712.0155]
24. D. Gaiotto, Monster symmetry and extremal CFTs [0801.0988]
25. P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory Graduate Texts in contemporary physics, Springer, U.S.A. (1997)
26. B. Farb and R.K. Dennis, Noncommutative algebra Graduate Texts in Mathematics 144, Springer, U.S.A. (1993)
27. A. Matsuo, Norton's trace formulae for the Griess algebra of a vertex operator algebra with larger symmetry 2001 Commun. Math. Phys. 224 565 [math.QA/0007169]
28. M.R. Gaberdiel and A. Neitzke, Rationality, quasirationality and finite W-algebras 2003 Comm. Math. Phys. 238 305 [hep-th/0009235]
29. M.R. Gaberdiel, S. Gukov, C.A. Keller, G.W. Moore and H. Ooguri, Extremal N = (2,2) 2D conformal field theories and constraints of modularity [0805.4216]
30. P. Goddard, Meromorphic conformal field theory in Infinite dimensional Lie algebras and Lie groups: Proceedings of the CIRM Luminy Conference, 1988 (World Scientific, Singapore) (1989) pg. 556 [DAMTP-89-01]
31. V.G. Kac, Vertex algebras for beginners American Mathematical Society, U.S.A. (1998)
32. M.R. Gaberdiel and P. Goddard, Axiomatic conformal field theory 2000 Comm. Math. Phys. 209 549 [hep-th/9810019]
33. M.R. Gaberdiel, An introduction to conformal field theory 2000 Rep. Prog. Phys. 63 607 [hep-th/9910156]