Instanton corrections to the universal hypermultiplet and automorphic forms on SU(2, 1)

Communications in Number Theory and Physics

Volumn 4, Issue 1, 2010, Pages 187-266

  Bao, Ling ^a   Kleinschmidt, Axel ^b   Nilsson, Bengt E W ^a   Persson, Daniel ^a,b   Pioline, Boris ^c  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b INTERNATIONAL SOLVAY INSTITUTES   (Belgium)

^c LPTHE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955895216     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2010.v4.n1.a5     Document Type: Article

References (92)

1. P. S. Aspinwall, Compactification, geometry and duality: N = 2 [arXiv:hep-th/0001001].
2. C. M. Hull and P. K. Townsend, Unity of superstring dualities,' Nucl. Phys. B 438 (1995), 109 [arXiv:hep-th/9410167].
3. E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995), 85 [arXiv:hep-th/9503124].
4. N. A. Obers and B. Pioline, U-duality and M-theory, Phys. Rept. 318 (1999), 113 [arXiv:hep-th/9809039].
5. M. B. Green and M. Gutperle, Effects of D-instantons, Nucl. Phys. B 498 (1997), 195 [arXiv:hep-th/9701093].
6. M. B. Green and J. H. Schwarz, Supersymmetrical String Theories, Phys. Lett. B 109 (1982), 444.
7. D. J. Gross and E. Witten, Superstring modifications of Einstein's equations, Nucl. Phys. B 277 (1986), 1.
8. E. D'Hoker, M. Gutperle and D. H. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B 722 (2005), 81 [arXiv:hep-th/0503180].
9. I. K. Kostov and P. Vanhove, Matrix string partition functions, Phys. Lett. B 444 (1998), 196 [arXiv:hep-th/9809130].
10. G. W. Moore, N. Nekrasov and S. Shatashvili, D-particle bound states and generalized instantons, Commun. Math. Phys. 209 (2000), 77 [arXiv:hep-th/9803265].
11. E. Kiritsis and B. Pioline, On R4 threshold corrections in type IIB string theory and (p, q) string instantons, Nucl. phys. B508, 509-534 (1997) [arXiv:hep-th/9707018].
12. M. B. Green and P. Vanhove, D-instantons, strings and M-theory, Phys. Lett. B 408 (1997), 122 [arXiv:hep-th/9704145].
13. N. Obers and B. Pioline, Eisenstein series and string thresholds, Commun. Math. Phys. 209 (2000), 275-324 [arXiv:hep-th/9903113].
14. C. Vafa and E. Zaslow (eds.), Mirror Symmetry, Clay Math. Monogr., 1 (2003), 929pp.
15. S. Cecotti, S. Ferrara and L. Girardello, Geometry of Type II Superstrings and the Moduli of Superconformal Field Theories, Int. J. Mod. Phys. A 4 (1989), 2475.
16. K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B456 (1995), 130-152 [arXiv:hep-th/9507158].
17. I. Antoniadis, S. Ferrara, R. Minasian and K. S. Narain, R4 couplings in M- and type II theories on Calabi-Yau spaces, Nucl. Phys. B507 (1997), 571-588 [arXiv:hep-th/9707013].
18. A. Strominger, Loop corrections to the universal hypermultiplet, Phys. Lett. B421 (1998), 139-148 [arXiv:hep-th/9706195].
19. H. Gunther, C. Herrmann and J. Louis, Quantum corrections in the hypermultiplet moduli space, Fortsch. Phys. 48 (2000), 119 [arXiv:hepth/9901137].
20. I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003), 5079-5102 [arXiv:hep-th/0307268].
21. N. Halmagyi, I. V. Melnikov and S. Sethi, Instantons, hypermultiplets and the heterotic string, JHEP 0707 (2007) 086 [arXiv:0704.3308[hep-th]].
22. S. M. Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1) (1982), 143-171.
23. A. Swann, Hyper-Kähler and quaternionic Kähler geometry, Math. Ann. 289 (3) (1991), 421-450.
24. C. LeBrun, Fano manifolds, contact structures, and quaternionic geometry, Int. J. Math. 6 (3) (1995), 419-437 [arXiv:dg-ga/9409001].
25. B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B568 (2000), 475-502 [arXiv:hep-th/9909228].
26. B. de Wit, M. Rocek and S. Vandoren, Hypermultiplets, hyperkähler cones and quaternion-Kähler geometry, JHEP 02, (2001), 039 [arXiv:hep-th/0101161].
27. S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, Linear perturbations of hyperkähler metrics, Lett. Math. Phys. 87 (2009), 225 [arXiv:0806.4620[hep-th]].
28. S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, Linear perturbations of quaternionic metrics, Commun. Math. Phys. 296 (2010), 353 [arXiv:0810.1675[hep-th]].
29. S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, D-instantons and twistors, JHEP 0903 (2009), 044 [arXiv:0812.4219[hep-th]].
30. D. Robles-Llana, M. Rocek, F. Saueressig, U. Theis and S. Vandoren, Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry, Phys. Rev. Lett. 98 (2007), 211602 [arXiv:hep-th/0612027].
31. D. Robles-Llana, F. Saueressig, U. Theis and S. Vandoren, Membrane instantons from mirror symmetry, Commun. Num. Theor. Phys. 1 (2007), 681 [arXiv:0707.0838[hep-th]].
32. S. Alexandrov, D-instantons and twistors: some exact results, J. Phys. A 42 (2009), 335402 [arXiv:0902.2761[hep-th]].
33. S. Alexandrov and F. Saueressig, Quantum mirror symmetry and twistors, JHEP 0909 (2009), 108 [arXiv:0906.3743[hep-th]].
34. B. Pioline and D. Persson, The automorphic NS5-brane, Commun. Num. Theor. Phys. 3 (4) (2009), 697-754 [arXiv:0902.3274[hep-th]].
35. N. Yui, Update on the modularity of Calabi-Yau varieties, Fields Inst. Commun., 38 (2003), 307-362.
36. P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985), 46.
37. A. Strominger and E. Witten, New Manifolds for superstring compactification, Commun. Math. Phys. 101 (1985), 341.
38. P. Candelas, E. Derrick and L. Parkes, Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B 407 (1993), 115 [arXiv:hep-th/9304045].
39. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys. 165 (1994), 311 [arXiv:hep-th/9309140].
40. P. S. Aspinwall and J. Louis, On the ubiquity of K3 fibrations in string duality, Phys. Lett. B 369 (1996), 233 [arXiv:hep-th/9510234].
41. S. Ferrara and S. Sabharwal, Dimensional reduction of type II superstrings, Class. Quant. Grav. 6 (1989), L77.
42. D. R. Morrison, Mirror symmetry and the type II string, Nucl. Phys. Proc. Suppl. 46 (1996), 146 [arXiv:hep-th/9512016].
43. C. Schoen, Varieties dominated by product varieties, Int. J. Math. 7 (4) (1996), 541-571.
44. G. W. Moore, Arithmetic and attractors, arXiv:hep-th/9807087.
45. S. Gukov and C. Vafa, Rational conformal field theories and complex multiplication, Commun. Math. Phys. 246 (2004), 181 [arXiv:hepth/0203213].
46. L. Bao, C. Colonnello, A. Kleinschmidt, B. E. W. Nilsson and D. Persson, Work in progress.
47. K. Becker and M. Becker, Instanton action for type II hypermultiplets, Nucl. Phys. B551 (1999), 102-116 [arXiv:hep-th/9901126].
48. N. Lambert and P.West, Duality groups, automorphic forms and higher derivative corrections, Phys. Rev. D75 (2007), 066002 [arXiv:hepth/0611318].
49. L. Bao, M. Cederwall and B. E. W. Nilsson, Aspects of higher curvature terms and U-duality, Class. Quant. Grav. 25 (2008), 095001 [arXiv:0706.1183[hep-th]].
50. Y. Michel and B. Pioline, Higher derivative corrections, dimensional reduction and Ehlers duality, JHEP 0709 (2007), 103 [arXiv:0706.1769[hep-th]].
51. C. Colonnello and A. Kleinschmidt, Ehlers symmetry at the next derivative order, JHEP 0708 (2007), 078 [arXiv:0706.2816[hep-th]].
52. L. Bao, J. Bielecki, M. Cederwall, B. E. W. Nilsson and D. Persson, U-duality and the compactified Gauss-Bonnet term, JHEP 0807 (2008), 048 [arXiv:0710.4907[hep-th]].
53. B. de Wit, N = 2 electric-magnetic duality in a chiral background, Nucl. Phys. Proc. Suppl. 49 (1996), 191 [arXiv:hep-th/9602060].
54. R. Bohm, H. Gunther, C. Herrmann and J. Louis, Compactification of type IIB string theory on Calabi-Yau threefolds, Nucl. Phys. B 569 (2000), 229 [arXiv:hep-th/9908007].
55. J. Manschot, Stability and duality in N=2 supergravity [arXiv:0906.1767[hep-th]].
56. E. Falbel, G. Francsics, P. D. Lax and J. R. Parker, Generators of a Picard modular group in two complex dimensions, arXiv:0911.1104[math.CV].
57. 2, Vienna, Preprint ESI 1273 (2003).
58. M. Gunaydin, K. Koepsell and H. Nicolai, The minimal unitary representation of E8(8), Adv. Theor. Math. Phys. 5 (2002), 923 [arXiv:hepth/0109005].
59. M. Gunaydin and O. Pavlyk, Minimal unitary realizations of exceptional U-duality groups and their subgroups as quasiconformal groups, JHEP 0501 (2005), 019 [arXiv:hep-th/0409272].
60. D. Kazhdan, B. Pioline and A. Waldron, Minimal representations, spherical vectors, and exceptional theta series. I, Commun. Math, Phys. 226 (2002), 1-40 [arXiv:hep-th/0107222].
61. D. Kazhdan and A. Polishchuk, Minimal representations: spherical vectors and automorphic functionals [arXiv:math/0209315 [math.RT]].
62. B. Pioline and A. Waldron, Automorphic forms: a physicist's survey, [arXiv:hep-th/0312068].
63. M. Gunaydin, A. Neitzke, O. Pavlyk and B. Pioline, Quasiconformal actions, quaternionic discrete series and twistors: SU(2,1) and G2(2), Commun. Math. Phys. 283 (2008), 169 [arXiv:0707.1669[hep-th]].
64. Y. Ishikawa, The generalized Whittaker functions for SU(2,1) and the Fourier expansion of automorphic forms, J. Math. Sci. Univ. Tokyo 6 (1999), 477-526.
65. R. P. Langlands, On the functional relations satisfied by Eisenstein series, Springer Lecture Notes in Mathematics, Vol. 544, 1-337, Springer, Berlin, 1976.
66. T. Orloff, Dirichlet series and automorphic forms on unitary groups, Trans. Am. Math. Soc. 290 (2) (1985), 431-456.
67. M. Henneaux, D. Persson and P. Spindel, Spacelike singularities and hidden symmetries of gravity, Living Rev. Rel. 11 (2008), 1 [arXiv:0710.1818[hep-th]].
68. D. Yasaki, Explicit reduction theory for SU(2, 1;Z[i]), [arXiv:math/0601071].
69. I. Bars and Z. J. Teng, The unitary irreducible representations of SU(2,1), J. Math. Phys. 31 (1990), 1576.
70. A. Borel, Automorphic form on SL(2, R), 1st edn., Cambridge University Press, Cambridge, 1997.
71. G. Zhang, Shimura invariant differential operators and their eigenvalues, Math. Ann. 319 (2) (2001), 235-265.
72. A. I. Vinogradov and L. A. Takhtadzhyan, Theory of Eisenstein series for the group SL(3, R) and its application to a binary problem, J. Sov. Math., 18 (3) (1983), 293.
73. N. V. Proskurin, Expansions of automorphic functions, Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN USSR, 116 (1982), 119-141.
74. P. Cartier, An introduction to zeta functions, in 'From Number Theory to Physics', eds. M. Waldschmidt et al., Springer, Berlin, 1995.
75. Series A086933 in the Online encyclopedia of integer sequences, http://www.research.att.com/~njas/sequences/
76. J. A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (6) (1965), 1033-1047.
77. L. Anguelova, M. Rocek and S. Vandoren, Quantum corrections to the universal hypermultiplet and superspace, Phys. Rev. D 70 (2004), 066001 [arXiv:hep-th/0402132].
78. D. Robles-Llana, F. Saueressig and S. Vandoren, String loop corrected hypermultiplet moduli spaces, JHEP 0603 (2006), 081 [arXiv:hepth/0602164].
79. S. Alexandrov, F. Saueressig and S. Vandoren, Membrane and fivebrane instantons from quaternionic geometry, JHEP, 09 (2006), 040 [arXiv:hep-th/0606259].
80. M. Przanowski, Locally hermite-Einstein, self-dual gravitational instantons, Acta Phys. Polon. B 14 (8) (1983), 625-627.
81. S. Alexandrov, B. Pioline and S. Vandoren, Self-dual Einstein Spaces, heavenly metrics and twistors, [arXiv:0912.3406[hep-th]].
82. B. Pioline and S. Vandoren, Large D-instanton effects in string theory, JHEP 0907 (2009), 008 [arXiv:0904.2303[hep-th]].
83. B. Pioline and A. Waldron, The automorphic membrane, JHEP 0406 (2004), 009 [arXiv:hep-th/0404018].
84. N. A. Obers and B. Pioline, Exact thresholds and instanton effects in string theory, Fortsch. Phys. 49 (2001), 359 [arXiv:hep-th/0101122].
85. B. H. Gross and N. R. Wallach, On quaternionic discrete series representations, and their continuations, J. Reine. Angew. Math. 481 (1996), 73-123.
86. R.-P. Holzapfel, Geometry and Arithmetic around Euler partial differential equations, D.Reidel Publishing Company, Springer, 1st edition, 1986.
87. E. Falbel and J. R. Parker, The geometry of the Eisenstein-Picard modular group, Duke Math. J. 131 (2) (2006), 249.
88. T. .M. Apostol, Introduction to analytic number theory, Springer, Berlin, 1976.
89. H. Neukirch, Algebraic number theory, Springer, Berlin, 2007.
90. N. Koblitz, p-adic Numbers, p-adic analysis and zeta functions, Springer, Berlin, 1977.
91. L. Brekke and P. G. O. Freund, p-adic numbers in physics, Phys. Rept. 233 (2003), 1-66.
92. T. Shintani, On automorphic forms on unitary groups of order 3, (preprint, 1979).