On the space of elliptic genera

Communications in Number Theory and Physics

Volumn 2, Issue 4, 2008, Pages 803-833

  Manschot, Jan ^a,b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954941957     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2008.v2.n4.a4     Document Type: Article

References (52)

1. J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986), 186.
2. O. Aharony, S. YaUI, O 8UO9UILnkielowicz and A.N. Schellekens, Charge sum rules in N = 2 theories, Nucl. Phys. B 418 (1994), 157, arXiv:hep-th/9311128.
3. E. Witten, Elliptic genera and quantum field theory, Commun. Math. Phys. 109 (1987), 525.
4. T. Eguchi, H. Oog UILuri, A. Taormina and S.K. Yang, Superconformal algebras and string compactification on manifolds with SU(N) holonomy, Nucl. Phys. B 315 (1989), 193.
5. V. GritseHU MIKYKU 8nko, Elliptic genus of calabi-yau manifolds and jacobi and siegel modular forms, math/9906190.
6. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein- Hawking entropy, Phys. Lett. B 379 (1996), 99ETV0I0R9UY=09, arXiv:hep-th/9601029.
7. J.M. Maldacena, A. R VG-0RTHYO0 0RTStrominger and E. Witten, Black hole entropy in M-theory, JHEP 9712 (1997), 002, arXiv:hep-th/9711053.
8. J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998), 231 (Int. J. Theor. Phys. 38 (1999) 1113), arXiv:hep-th/9711200.
9. M. Cvetic and F. Larsen, Near horizon geometry of rotating black holes in five dimensions, Nucl. Phys. B 531 (1998), 239, arXiv:hepth/ 9805097.
10. R. DijkgRTY-I -0RT9Y0 na, G.W. Moore and E.P. Verlinde, A black hole farey tail, arXiv:hep-th/0005003.
11. J. Manschot and G.W. Moore, A modern farey tail, arXiv:0712.0573 [hep-th].
12. D. Niebur, Construction of automorphic forms and integrals, Trans. Amer. Math. Soc. 191 (1974), 373-385.
13. 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, arXiv:0805.4216 [hep-th].
14. M. Eichler and D. Zagier, The theory of Jacobi forms, Birkhäuser, 1985.
15. N.P. Skoruppa, Über den Zusamme TREIJ0[-89uq=085y hu3ny.p5 'hlp]o4j et Modulformen halbganzen Gewichts, Dissertation, Universität Bonn, 1984.
16. R. Minasian, G.W. Moore and D. Tsimpis, Calabi-Yau black holes and (0,4) sigma models, Commun. Math. Phys. 209 (2000), 325, arXiv:hepth/ 9904217.
17. D. Gaiotto, A. Strominger and X. Yin, The M5-brane elliv t8oehtheiu vhiuqheiru vtty and BPS states, JHEP 0708, 070 (2007)
18. P. Kraus and F. Larsen, Partre oipokdf ijoirtj hoioijrtk vl;jtwe,sciogravity, JHEP 0701 (2007), 002, arXiv:hep-th/0607138.
19. J. de Boer, M.C.N. Cheng, R. Dijkgraaf, J. Manschot and E. Verlinde, A farey tail for attractor black holes, JHEP 0611 (2006), 024 arXiv:hepth/ 0608059.
20. T. Kawai, Y. Yamada and S.K. Yang, Elliptic genera and N=2 superconformal field theory, Nucl. Phys. B 414 (1994), 191, arXiv:hep-th/ 9306096.
21. N. Koblitz, Introduction ttjhojojoigfo9hodjcvbmkvcmblkmkvbhojkkmkljmkjforms, Springer-Verlag, 1993.
22. M.I. Knopp, Some new results on the Eichler cohomology of automorphic forms, Bull. Amer. Math. Soc. 80 (1974), 607-632.
23. E. Witten, Three-dimensional gravity revisited, arXiv:0706.3359 [hep-th].
24. P. Sarnak, Some applications of modular forms, Cambridge University Press, 1990.
25. P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley and Sons, 1978.
26. R.E. Borcherds, The Gross-Kohnen-Zagier theorem in higher dimensions, Duke Math. J. 97 (1999), 219-233.
27. W. Eholzer and N.P. Skoruppa, Modular invariance and uniqueness of conformal characters, Commun. Math. Phys. 174 (1995), 117, arXiv:hep-th/9407074.
28. P. Bantay and T. Gannon, ery o-ik45yoiib 00-596iuy9i f0to0diojk0ijkoijdgvui9yar group and the hypergeometric equation, arXiv:0705.2467 [math.NT].
29. D. Zagier, The Eichler-Selberg trace formula on SL2(Z), Appendix in S. Lang Introduction to modular forms, Springer-Verlag, 1976; Correction in modular functions of one variable VI, Lect. in Math., 627, Springer-Verlag, 1976.
30. T.M. Apostol, Introduction to analytic number theory. Springer-Verlag, 1976.
31. N.P. Skoruppa and D. Zagier, Jacotyu tybjhbtfar forms, Invent. Math. 94 (1988), 113.
32. N.P. Skoruppa and D. Zagier, A trace formula for Jacobi forms, J. Reine Angew. Math. 393 (1989), 168.
33. N.P. Skoruppa, Memorandum on dimension formulas for spaces of Jacobi forms, arXiv:0711.0632 [math.NT].
34. J. Kramer, A geometrical approach to the theory of Jacobi forms, Comp. Math. 79 (1991), 1.
35. M.R. Gaberdiel and C.A. Keller, Modular differential equations and null vectors, arXiv:0804.0489 [hep-th].
36. C. Vafa and E. Witten, A strong couplinkhk bn6y444s rgtS duality, Nucl. Phys. B 431 (1994), 3, arXiv:hep-th/9408074.
37. D. Gaiotto and X. Yin, Examples of M5-brane elliptic genera, JHEP 0711 (2007), 004, arXiv:hep-th/0702012.
38. F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, arXiv:hep-th/0702146.
39. J.M. Maldacena, G.W. Moore and A. Strominger, Counting BPS black holes in toroidal type II string theory, arXiv:hep-th/9903163.
40. D.S. Freed and E. Witten, Anomalies in string theory with D-branes, arXiv:hep-th/9907189.
41. C. Montonen and D.I. Olive, Magnetic monopoles as gauge particles? Phys. Lett. B 72 (1977), 117.
42. P. Goddard, J. Nuyts and D.I. Olive, Gauge theories and magnetic charge, Nucl. Phys. B 125 (1977), 1.
43. E. Witten, AdS/CFT correspondence and topological field theory, JHEP 9812 (1998), 012, arXiv:hep-th/9812012.
44. J.M. Maldacena, G.W. Moore and N. Seiberg, D-brane charges in fivebrane backgrounds, JHEP 0110 (2001), 005, arXiv:hep-th/0108152.
45. G.W. Moore, Anomalies, Gauss laws, and page charges in M-theory, C. R. Phys. 6 (2005), 251, arXiv:hep-th/0409158.
46. A. Ogg, Modular forms and Dirichlet series, W. A. Benjamin, Inc., 1969.
47. L. Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990), 193.
48. K. Yoshioka, The Betti numbers of the moduli space of stable sheaves of rank 2 on P2, J. Reine. Angew. Math. 453 (1994), 193.
49. A.A. Klyachko, Moduli of vector bundles and numbers of classes, Funct. Anal. Appl. 25 (1991), 67.
50. D. Zagier, Nombres de classes et formes modulaires de poids 3/2, C.R. Acad. Sci. Paris 281 (1975), 883.
51. F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces modular forms of Nebentypus, Invent. Math. 36 (1976), 57.
52. J.A. Minahan, D. Nemeschansky, C. Vafa and N.P. Warner, E-strings and N = 4 topological Yang-Mills theories, Nucl. Phys. B 527 (1998), 581, arXiv:hep-th/9802168.