Topological wave functions and heat equations

Journal of High Energy Physics

Volumn 2006, Issue 12, 2006, Pages

  Günaydin, Murat ^a   Neitzke, Andrew ^b   Pioline, Boris ^c,d  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c LPTHE   (France)

^d LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

Black Holes in String Theory; Topological Strings

Indexed keywords

EID: 33846177579     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/12/070     Document Type: Review

References (86)

1. G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black-hole entropy 1999 Phys. Lett. B 451 309 [hep-th/9812082]
2. G. Lopes Cardoso, B. de Wit and T. Mohaupt, Deviations from the area law for supersymmetric black holes 2000 Fortschr. Phys. 48 49 [hep-th/9904005]
3. G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes 2000 Nucl. Phys. B 567 87 [hep-th/9906094]
4. H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string 2004 Phys. Rev. D 70 106007 [hep-th/0405146]
5. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories 1993 Nucl. Phys. B 405 279 [hep-th/9302103]
6. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes 1994 Comm. Math. Phys. 165 311 [hep-th/9309140]
7. E. Witten, Quantum background independence in string theory [hep-th/9306122]
8. E.P. Verlinde, Attractors and the holomorphic anomaly [hep-th/0412139]
9. M. Eichler and D. Zagier, The theory of Jacobi forms, vol. 55 of Progress in mathematics Birkhäuser Boston Inc., Boston, MA, 1985
10. R. Berndt and R. Schmidt, Elements of the representation theory of the Jacobi group, vol. 163 of Progress in mathematics Birkhäuser Verlag, Basel, 1998
11. M. Günaydin, A. Neitzke, B. Pioline and A. Waldron, BPS black holes, quantum attractor flows and automorphic forms 2006 Phys. Rev. D 73 084019 [hep-th/0512296]
12. S. Hosono, M.H. Saito and A. Takahashi, Holomorphic anomaly equation and BPS state counting of rational elliptic surface 1999 Adv. Theor. Math. Phys. 3 177 [hep-th/9901151]
13. A.N. Todorov, Witten's geometric quantization of the moduli of CY threefolds [math.AG/0004043]
14. A.A. Gerasimov and S.L. Shatashvili, Towards integrability of topological strings, I. Three- forms on Calabi-Yau manifolds 2004 J. High Energy Phys. JHEP11(2004)074 [hep-th/0409238]
15. M.-X. Huang and A. Klemm, Holomorphic anomaly in gauge theories and matrix models [hep-th/0605195]
16. M. Aganagic, V. Bouchard and A. Klemm, Topological strings and (almost) modular forms [hep-th/0607100]
17. R. Dijkgraaf, E.P. Verlinde and M. Vonk, On the partition sum of the NS five-brane [hep-th/0205281]
18. N.M.J. Woodhouse, Geometric quantization Oxford Mathematical Monographs, The Clarendon Press (Oxford University Press), New York, second ed., 1992, Oxford Science Publications
19. W.D. Kirwin and S. Wu, Geometric quantization, parallel transport and the Fourier transform [math.SG/0409555]
20. S. Axelrod, S. Della Pietra, and E. Witten, Geometric quantization of Chern-Simons gauge theory, 1991 J. Diff. Geom. 33 787-902
21. D. Mumford, Tata lectures on theta, I vol. 28 of Progress in Mathematics Birkhäuser Boston Inc., Boston, MA, 1983, with the assistance of C. Musili, M. Nori, E. Previato and M. Stillman
22. M. Günaydin, G. Sierra and P.K. Townsend, Exceptional supergravity theories and the magic square 1983 Phys. Lett. B 133 72
23. M. Günaydin, G. Sierra and P.K. Townsend, The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras 1984 Nucl. Phys. B 242 244
24. M. Günaydin, G. Sierra and P.K. Townsend, Gauging the D = 5 Maxwell-Einstein supergravity theories: more on Jordan algebras 1985 Nucl. Phys. B 253 573
25. S. Ferrara and M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory 1998 Int. J. Mod. Phys. A 13 2075 [hep-th/9708025]
26. M. Günaydin, K. Koepsell and H. Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups 2001 Comm. Math. Phys. 221 57 [hep-th/0008063]
27. M. Günaydin, Unitary realizations of U-duality groups as conformal and quasiconformal groups and extremal black holes of supergravity theories 2005 AIP Conf. Proc. 767 268-287 [hep-th/0502235]
28. M. Günaydin and O. Pavlyk, Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups 2005 J. High Energy Phys. JHEP08(2005)101 [hep-th/0506010]
29. S. Bellucci, S. Ferrara, M. Günaydin and A. Marrani, Charge orbits of symmetric special geometries and attractors 2006 Int. J. Mod. Phys. A 21 5043 [hep-th/0606209]
30. S. Ferrara, J.A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry 1995 Phys. Lett. B 361 59 [hep-th/9505162]
31. A. Klemm and M. Marino, Counting BPS states on the enriques Calabi-Yau [hep-th/0512227]
32. D. Maulik and R. Pandharipande, New calculations in Gromov-Witten theory [math.ag/0601395]
33. A. Sen and C. Vafa, Dual pairs of type-II string compactification 1995 Nucl. Phys. B 455 165 [hep-th/9508064]
34. K. McCrimmon, The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras, 1969 Trans. Amer. Math. Soc. 139 495-510
35. 8 zur Oktavenebene. I, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16 (1954) 218-230
36. I. Kantor and I. Skopets, Some results on Freudenthal triple systems, 1982 Sel. Math. Sov. 2 293
37. K. Meyberg, Eine Theorie der Freudenthalschen Tripelsysteme. I, II, 1968 Nederl. Akad. Wetensch. Proc. Ser. A 71 = Indag. Math. 30 162-174, 175-190
38. H. Freudenthal, Lie groups in the foundations of geometry Advances in Math. 1 (1964), no. fasc. 2, 145-190
39. 7, 1969 J. Reine Angew. Math. 236 79-102
40. J.C. Ferrar, Strictly regular elements in Freudenthal triple systems, 1972 Trans. Amer. Math. Soc. 174 313-331 (1973)
41. 7, 1972 Trans. Amer. Math. Soc. 167 49-58
42. E. Cremmer and A. Van Proeyen, Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings 1985 Class. Quantum Grav. 2 445
43. E. Cremmer et al., Vector multiplets coupled to N = 2 supergravity: super-Higgs effect, flat potentials and geometric structure 1985 Nucl. Phys. B 250 385
44. B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces 1992 Comm. Math. Phys. 149 307 [hep-th/9112027]
45. B. de Wit and A. Van Proeyen, Broken sigma model isometries in very special geometry 1992 Phys. Lett. B 293 94 [hep-th/9207091]
46. B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries 1993 Nucl. Phys. B 400 463 [hep-th/9210068]
47. J. Faraut and A. Korányi, Analysis on symmetric cones, Oxford Mathematical Monographs. The Clarendon Press (Oxford University Press), New York, 1994. Oxford Science Publications
48. D.V. Alekseevsky and V. Cortés, Classification of stationary compact homogeneous special pseudo-Kähler manifolds of semisimple groups, Proc. London Math. Soc. (3) 81 (2000), no. 1, 211-230
49. M. Günaydin, Generalized conformal and superconformal group actions and jordan algebras 1993 Mod. Phys. Lett. A 8 1407 [hep-th/9301050]
50. B.H. Gross, A remark on tube domains Math. Res. Lett. 1 (1994), no. 1, 1-9
51. M. Günaydin, AdS/CFT dualities and the unitary representations of non- compact groups and supergroups: wigner versus dirac [hep-th/0005168]
52. A. Polishchuk, Abelian varieties, theta functions and the Fourier transform, vol. 153 of Cambridge Tracts in Mathematics, (Cambridge University Press, Cambridge), 2003
53. I. Zharkov, Theta functions for indefinite polarizations 2004 J. Reine Angew. Math. 573 95-116, [math.AG/0011112]
54. M. Günaydin, B. Pioline, M. Rocek, and S. Vandoren. To appear
55. A. Joseph, Minimal realizations and spectrum generating algebras 1974 Comm. Math. Phys. 36 325
56. D. Kazhdan and G. Savin, The smallest representation of simply laced groups in Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part I (Ramat Aviv, 1989) vol. 2 of Israel Math. Conf. Proc. pp. 209-223, Weizmann, Jerusalem, 1990
57. 2, 1993 J. Reine Angew. Math. 434 115-126
58. R. Brylinski and B. Kostant, Minimal representations, geometric quantization, and unitarity Proc. Nat. Acad. Sci. U.S.A. 91 (1994), no. 13, 6026-6029
59. B.H. Gross and N.R. Wallach, A distinguished family of unitary representations for the exceptional groups of real rank =4, in Lie theory and geometry vol. 123 of Progr. Math., pp. 289-304, Birkhäuser Boston, Boston, MA, 1994
60. 8, in Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswick, NJ, 1993) vol. 131 of Progr. Math. pp. 13-63, Birkhäuser Boston, Boston, MA, 1995
61. D. Kazhdan and A. Polischuk, Minimal representations, spherical vectors and automorphic functionals, [math.RT/0209315]
62. W.T. Gan and G. Savin, On minimal representations 2005 Represent. Theory 9 46-93 (electronic)
63. 4 couplings, the fundamental membrane and exceptional theta correspondences 2001 J. High Energy Phys. JHEP03(2001)036 [hep-th/0102123]
64. D. Kazhdan, B. Pioline and A. Waldron, Minimal representations, spherical vectors and exceptional theta series, I 2002 Comm. Math. Phys. 226 1 [hep-th/0107222]
65. 8 2002 Adv. Theor. Math. Phys. 5 923 [hep-th/0109005]
66. B. Pioline and A. Waldron, The automorphic membrane 2004 J. High Energy Phys. JHEP06(2004)009 [hep-th/0404018]
67. M. Günaydin and O. Pavlyk, Minimal unitary realizations of exceptional u-duality groups and their subgroups as quasiconformal groups 2005 J. High Energy Phys. JHEP01(2005)019 [hep-th/0409272]
68. B. Pioline, BPS black hole degeneracies and minimal automorphic representations 2005 J. High Energy Phys. JHEP08(2005)071 [hep-th/0506228]
69. M. Günaydin and O. Pavlyk, A unified approach to the minimal unitary realizations of noncompact groups and supergroups 2006 J. High Energy Phys. JHEP09(2006)050 [hep-th/0604077]
70. W. T. Gan, An automorphic theta module for quaternionic exceptional groups Canad. J. Math. 52 (2000), no. 4, 737-756
71. D. Ginzburg, S. Rallis, and D. Soudry, On the automorphic theta representation for simply laced groups 1997 Israel J. Math. 100 61-116
72. M. Weissman, The Fourier-Jacobi map and small representations, 2003 Represent. theory 7 275-299 (electronic)
73. B. de Wit and F. Saueressig, Off-shell N = 2 tensor supermultiplets 2006 J. High Energy Phys. JHEP09(2006)062 [hep-th/0606148]
74. A. Kapustin, Gauge theory, topological strings and s-duality 2004 J. High Energy Phys. JHEP09(2004)034 [hep-th/0404041]
75. H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds 1996 Nucl. Phys. B 463 55 [hep-th/9511164]
76. N. Nekrasov, H. Ooguri and C. Vafa, S-duality and topological strings 2004 J. High Energy Phys. JHEP10(2004)009 [hep-th/0403167]
77. A. Iqbal, N. Nekrasov, A. Okounkov and C. Vafa, Quantum foam and topological strings [hep-th/0312022]
78. D. Maulik, N. A. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory, [math.AG/0312059]
79. D. Maulik, N. A. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory, II, [math.AG/0406092]
80. R. P. Thomas, "Gauge theories on Calabi-Yau manifolds," 1997. Available as of July 2006 at http://www.ma.ic.ac.uk/∼rpwt/thesis.pdf
81. H. Ooguri, C. Vafa and E.P. Verlinde, Hartle-Hawking wave-function for flux compactifications 2005 Lett. Math. Phys. 74 311 [hep-th/0502211]
82. E. Witten, Five-brane effective action in M-theory 1997 J. Geom. Phys. 22 103 [hep-th/9610234]
83. R. Dijkgraaf, Mirror symmetry and elliptic curves in The moduli space of curves (Texel Island, 1994) vol. 129 of Progr. Math. pp. 149-163, Birkhäuser Boston, Boston, MA, 1995
84. M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, in The moduli space of curves (Texel Island, 1994) vol. 129 of Progr. Math. pp. 165-172, Birkhäuser Boston, Boston, MA, 1995
85. N. Berkovits and C. Vafa, N = 4 topological strings 1995 Nucl. Phys. B 433 123 [hep-th/9407190]
86. H. Ooguri and C. Vafa, All loop N = 2 string amplitudes 1995 Nucl. Phys. B 451 121 [hep-th/9505183]