Generalized kac-moody algebras from CHL dyons

Journal of High Energy Physics

Volumn 2009, Issue 4, 2009, Pages

  Govindarajan, Suresh ^a   Krishna, K Gopala ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

^b INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

Black holes in string theory; D branes; String duality; Superstrings and heterotic strings

Indexed keywords

EID: 67649497148     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2009/04/032     Document Type: Article

References (62)

1. A. Strominger and C. Vafa, 1996 Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 99 [hep-th/9601029]
2. M.J. Duff, J.T. Liu and J. Rahmfeld, 1996 Four-dimensional string-string-string triality, Nucl. Phys. B 459 125 [hep-th/9508094]
3. R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, 1997 Counting dyons in N=4 string theory, Nucl. Phys. B 484 543 [hep-th/9607026]
4. V.A. Gritsenko, V.V. Nikulin, 1997 Siegel automorphic form corrections of some lorentzian Kac-Moody Lie algebras, Amer. J. Math. 119 181 [alg-geom/9504006]
5. J.A. Harvey and G.W. Moore, 1996 Algebras, BPS states and strings, Nucl. Phys. B 463 315 [hep-th/9510182]
6. J.A. Harvey and G.W. Moore, 1998 On the algebras of BPS states, Commun. Math. Phys. 197 489 [hep-th/9609017]
7. M.C.N. Cheng and E.P. Verlinde, 2008 Wall crossing, discrete attractor flow and Borcherds algebra, SIGMA 4 068 [0806.2337]
8. S. Chaudhuri, G. Hockney and J.D. Lykken, 1995 Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 2264 [hep-th/9505054]
9. D.P. Jatkar and A. Sen, 2006 Dyon spectrum in CHL models, J. High Energy Phys. JHEP04(2006)018 [hep-th/0510147]
10. A. Sen, 2005 Black holes, elementary strings and holomorphic anomaly, J. High Energy Phys. JHEP07(2005)063 [hep-th/0502126]
11. R. Borcherds, 1990 The Monster Lie algebra, Adv. Math. 83 30
12. P. Niemann, 2002 Some generalized Kac-Moody algebras with known root multiplicities, Mem. Amer. Math. Soc. 157 746 [math.QA/0001029]
13. J.H. Schwarz and A. Sen, 1994 Duality symmetric actions, Nucl. Phys. B 411 35 [hep-th/9304154]
14. 6, J. High Energy Phys. JHEP03(2008)022 [0712.0043]
15. M. Cveti and D. Youm, 1996 Dyonic BPS saturated black holes of heterotic string on a six torus, Phys. Rev. D 53 584 [hep-th/9507090]
16. W. Lerche and S. Stieberger, 1999 1/4 BPS states and non-perturbative couplings in N=4 string theories, Adv. Theor. Math. Phys. 3 1539 [hep-th/9907133]
17. J.R. David, D.P. Jatkar and A. Sen, 2006 Product representation of dyon partition function in CHL models, J. High Energy Phys. JHEP06(2006)064 [hep-th/0602254]
18. A. Dabholkar, F. Denef, G.W. Moore and B. Pioline, 2005 Exact and asymptotic degeneracies of small black holes, J. High Energy Phys. JHEP08(2005)021 [hep-th/0502157]
19. A. Dabholkar, F. Denef, G.W. Moore and B. Pioline, 2005 Precision counting of small black holes, J. High Energy Phys. JHEP10(2005)096 [hep-th/0507014]
20. A. Dabholkar, 2005 Exact counting of black hole microstates, Phys. Rev. Lett. 94 241301 [hep-th/0409148]
21. A. Sen, 2006 Entropy function for heterotic black holes, J. High Energy Phys. JHEP03(2006)008 [hep-th/0508042]
22. A. Dabholkar and S. Nampuri, 2007 Spectrum of dyons and black holes in CHL orbifolds using Borcherds lift, J. High Energy Phys. JHEP11(2007)077 [hep-th/0603066]
23. J.R. David and A. Sen, 2006 CHL dyons and statistical entropy function from D1-D5 system, J. High Energy Phys. JHEP11(2006)072 [hep-th/0605210]
24. D. Shih, A. Strominger and X. Yin, 2006 Recounting dyons in N=4 string theory, J. High Energy Phys. JHEP10(2006)087 [hep-th/0505094]
25. R. Dijkgraaf, G.W. Moore, E.P. Verlinde and H.L. Verlinde, 1997 Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 197 [hep-th/9608096]
26. rd ed., Cambridge University Press, Cambridge U.K.
27. A.J. Feingold and I.B. Frenkel, 1983 A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2, Math. Ann. 263 87
28. A.J. Feingold and H. Nicolai, Subalgebras of hyperbolic Kac-Moody algebras [math/0303179]
29. J. Lepowsky and S. Milne, 1978 Lie algebraic approaches to classical partition identities, Adv. Math. 29 15
30. I.G. MacDonald, 1972 Affine root systems and Dedekind's η-function, Invent. Math 15 91
31. J. Lepowsky and H. Garland, 1976 Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 37
32. R. Borcherds, 1988 Generalized Kac-Moody algebras, J. Algebra 115 501
33. R. Borcherds, 1992 Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 405
34. E. Jurisich, 1996 An exposition of generalized Kac-Moody algebras, Contemp. Math. 194 121
35. H. Aoki and T. Ibukiyama, 2005 Simple graded rings of Siegel modular forms, differential operators and Borcherds products, Internat. J. Math. 16 3 249
36. A. Dabholkar and D. Gaiotto, 2007 Spectrum of CHL dyons from genus-two partition function, J. High Energy Phys. JHEP12(2007)087 [hep-th/0612011]
37. A. Sen, 2007 Walls of marginal stability and dyon spectrum in N=4 supersymmetric string theories, J. High Energy Phys. JHEP05(2007)039 [hep-th/0702141]
38. A. Sen, 2007 Rare decay modes of quarter BPS dyons, J. High Energy Phys. JHEP10(2007)059 [0707.1563]
39. A. Mukherjee, S. Mukhi and R. Nigam, 2007 Dyon death eaters, J. High Energy Phys. JHEP10(2007)037 [0707.3035]
40. A. Mukherjee, S. Mukhi and R. Nigam, Kinematical analogy for marginal dyon decay, [0710.4533]
41. M.C.N. Cheng and A. Dabholkar, Borcherds-Kac-Moody symmetry of N=4 dyons, [0809.4258]
42. V.A. Gritsenko and V.V. Nikulin, 1996 The Igusa modular forms and ''the simplest'' lorentzian Kac-Moody algebras, Mat. Sb. 187 27 [alg-geom/9603010]
43. V.A. Gritsenko and V.V. Nikulin, 1996 Sb. Math. 187 1601
44. A. Garbagnati and A. Sarti, 2007 Symplectic automorphisms of prime order on K3 surfaces, J. Algebra 318 323 [math/0603742]
45. A. Garbagnati and A. Sarti, Elliptic fibrations and symplectic automorphisms on K3 surfaces, [0801.3992]
46. V. Gritsenko, 1999 Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms, Algebra i Analiz 11 100 [math/9906190]
47. V. Gritsenko, 2000 St. Petersburg Math. J. 11 781
48. R. Gopakumar and C. Vafa, M-theory and topological strings. I, [hep-th/9809187]
49. R. Gopakumar and C. Vafa, M-theory and topological strings. II, [hep-th/9812127]
50. B. Young, Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds, with an appendix by J. Bryan, [0802.2948]
51. S. Raghavan, 1976 Cusp forms of degree 2 and weight 3, Math. Ann. 224 149
52. M. Eichler and D. Zagier, 1985 The theory of Jacobi forms, Birkhäuser, Germany
53. H. Maa, 1979 ber eine Spezialschar von Modulformen zweiten Grades, Inv. Math. 52 95
54. H. Maa, 1979 ber eine Spezialschar von Modulformen zweiten Grades. II, Inv. Math. 53 249
55. H. Maaß, 1979 ber eine Spezialschar von Modulformen zweiten Grades. III, Inv. Math. 53 255
56. We found it useful to refer to the online encyclopedias: http://planetmath.org/encyclopedia/DirichletCharacter.html as well as http://en.wikipedia.org/wiki/Dirichlet-character
57. I. Reiner, 1955 Real linear characters of the symplectic modular group, Proc. Amer. Math. Soc. 6 987
58. H. Maaß, 1964 Die Multiplikatorsysteme zur Siegelschen Modulgruppe, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 125
59. M. Manickam and B. Ramakrishnan, 1993 On Saito-Kurokawa descent for congruence subgroups, Manuscripta Math. 81 161
60. M. Manickam and B. Ramakrishnan, 2002 On Saito-Kurokawa correspondence of degree two for arbitrary level, J. Ramanujan Math. Soc. 17 149
61. H. Aoki, A note on additive lifts of Jacobi forms with levels, under preparation
62. H. Maaß, 1980 ber ein Analogon zur Vermutung yon Saito-Kurokawa, Inv. Math. 60 85