Strings and arithmetic

Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

Volumn , Issue , 2007, Pages 303-359

  Moore, Gregory ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954893671     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-30308-4_8     Document Type: Chapter

References (110)

1. D. Kutasov, J. Marklof, and G. Moore,"Melvin models and Diophantine Approximation," Commun. Math. Phys. 256: 491-511, 2005 [arXiv:hep-th/ 0407150]
2. R. Dijkgraaf, J. M. Maldacena, G. W. Moore and E. Verlinde,"A black hole farey tail," arXiv:hep-th/0005003.
3. Y. I. Manin and M. Marcolli,"Holography principle and arithmetic of algebraic curves," Adv. Theor. Math. Phys. 5, 617 (2002) [arXiv:hep-th/0201036].
4. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz,"Large N field theories, string theory and gravity," Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111].
5. I. R. Klebanov,"TASI lectures: Introduction to the AdS/CFT correspondence," arXiv:hep-th/0009139.
6. K. Skenderis,"Lecture notes on holographic renormalization," Class. Quant. Grav. 19, 5849 (2002) [arXiv:hep-th/0209067].
7. N. Seiberg and E. Witten,"The D1/D5 system and singular CFT," JHEP 9904, 017 (1999) [arXiv:hep-th/9903224].
8. F. Larsen and E. J. Martinec, JHEP 9906, 019 (1999) [arXiv:hep-th/ 9905064].
9. F. Larsen and E. J. Martinec, JHEP 9911, 002 (1999) [arXiv:hep-th/ 9909088].
10. E. Martinec, Lectures given at the Komaba workshop, November 1999; notes available at http://theory.uchicago.edu/∼ejm/japan99.ps
11. N. Seiberg and A. Schwimmer,"Comments on the N=2, N=3, N=4 su-perconformal algebras in two dimensions," Phys. Lett. 184B(1987)191
12. M. Eichler and D. Zagier, The theory of Jacobi forms, Birkḧauser 1985
13. E. Witten,"Elliptic Genera and Quantum Field Theory," Commun. Math. Phys. 109(1987)525; "The index of the Dirac operator in loop space," Proceedings of the conference on elliptic curves and modular forms in algebraic topology, Princeton NJ, 1986.
14. G. Segal,"Elliptic cohomology," Asterisque 161-162(1988) exp. no. 695, 187-201
15. O. Alvarez, T. P. Killingback, M. L. Mangano and P. Windey,"String Theory And Loop Space Index Theorems," Commun. Math. Phys. 111, 1 (1987).
16. O. Alvarez, T. P. Killingback, M. L. Mangano and P. Windey,"The Dirac-Ramond Operator In String Theory And Loop Space Index Theorems," UCB-PTH-87/11 Invited talk presented at the Irvine Conf. on Non-Perturbative Methods in Physics, Irvine, Calif., Jan 5-9, 1987
17. R. Dijkgraaf,"Instanton strings and hyperKaehler geometry," Nucl. Phys. B 543, 545 (1999) [arXiv:hep-th/9810210].
18. W. Lerche and N. P. Warner, ' 'Index Theorems In N=2 Superconformal Theories," Phys. Lett. B 205, 471 (1988).
19. W. Lerche, B. E. W. Nilsson, A. N. Schellekens and N. P. Warner,"Anomaly Cancelling Terms From The Elliptic Genus," Nucl. Phys. B 299, 91 (1988).
20. K. Pilch and N. P. Warner,"String Structures And The Index Of The Dirac-Ramond Operator On Orbifolds," Commun. Math. Phys. 115, 191 (1988).
21. K. Pilch, A. N. Schellekens and N. P. Warner,"Path Integral Calculation Of String Anomalies," Nucl. Phys. B 287, 362 (1987).
22. A. N. Schellekens and N. P. Warner,"Anomaly Cancellation And Self-dual Lattices," Phys. Lett. B 181, 339 (1986).
23. A. N. Schellekens and N. P. Warner,"Anomalies And Modular Invariance In String Theory," Phys. Lett. B 177, 317 (1986).
24. T. Kawai, Y. Yamada and S. K. Yang, Nucl. Phys. B 414 (1994) 191 [arXiv:hep-th/9306096].
25. P. Windey,"The New Loop Space Index Theorems And String Theory," Lectures given at 25th Ettore Majorana Summer School for Subnuclear Physics, Erice, Italy, Aug 6-14, 1987
26. R. Dijkgraaf, G. Moore, E. Verlinde and H. Verlinde,"Elliptic Genera of Symmetric Products and Second Quantized Strings," Com-mun.Math.Phys. 185 (1997) 197-209
27. T. Kawai,"K3 surfaces, Igusa cusp form and string theory," hep-th/9710016
28. J. A. Harvey and G. W. Moore,"Algebras, BPS States, and Strings," Nucl. Phys. B 463, 315 (1996) [arXiv:hep-th/9510182].
29. H. Rademacher, Topics in Analytic Number Theory
30. H. Rademacher, Lectures on Elementary Number Theory, Robert E. Krieger Publishing Co., 1964
31. T. Apostol, Modular Functions and Dirichlet Series in Number Theory, Springer Verlag 1990
32. A. Strominger and C. Vafa,"Microscopic Origin of the Bekenstein-Hawking Entropy," hep-th/9601029; Phys.Lett. B379 (1996) 99-104
33. M. Bañados. C. Teitelboim, and J. Zanelli,"The Black Hole in Three Dimensional Space Time," hep-th/9204099; Phys.Rev.Lett. 69 (1992) 1849-1851
34. S. Carlip, Quantum gravity in 2+1 dimensions, Cambridge University Press, 1998
35. 3 black holes and a stringy exclusion principle," hep-th/9804085
36. 3 and 2d conformal field theory," hep-th/9806104; "Large N Elliptic Genus and AdS/CFT Correspondence," hep-th/9812240
37. E. Witten,"(2+1)-Dimensional Gravity As An Exactly Soluble System," Nucl. Phys. B 311, 46 (1988).
38. 3," hep-th/9804166
39. H. Lu, C. N. Pope and E. Sezgin,"SU(2) reduction of six-dimensional (1, 0) supergravity," arXiv:hep-th/0212323.
40. G. Arutyunov, A. Pankiewicz and S. Theisen,"Cubic couplings in D = 6 N = 4b supergravity on AdS(3) x S(3)," Phys. Rev. D 63, 044024 (2001) [arXiv:hep-th/0007061].
41. M. Cvetíc and F. Larsen,"Near Horizon Geometry of Rotating Black Holes in Five Dimensions," hep-th/9805097
42. O. Lunin, J. Maldacena and L. Maoz,"Gravity solutions for the D1-D5 system with angular momentum," arXiv:hep-th/0212210.
43. J.C. Breckenridge, D.A. Lowe, R.C. Myers, A.W. Peet, A. Strominger, C. Vafa,"Macroscopic and Microscopic Entropy of Near-Extremal Spinning Black Holes," hep-th/9603078; Phys.Lett. B381 (1996) 423-426
44. M. Cvetic and D. Youm,"General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String," hep-th/9603100; Nucl.Phys. B476 (1996) 118-132
45. A. Strominger,"Black hole entropy from near-horizon microstates," JHEP 9802, 009 (1998) [arXiv:hep-th/9712251].
46. T. Banks,"Supersymmetry, the cosmological constant and a theory of quantum gravity in our universe," arXiv:hep-th/0305206.
47. T. Banks,"A critique of pure string theory: Heterodox opinions of diverse dimensions," arXiv:hep-th/0306074.
48. E. Witten,"Anti-de Sitter Space and holography," hep-th/9802150; "Anti-de Sitter space, thermal phase transition, and confinement in gauge theories," hep-th/9803131
49. J. M. Maldacena,"Eternal black holes in Anti-de-Sitter," arXiv:hep-th/0106112.
50. V. Balasubramanian, A. Naqvi and J. Simon,"A multi-boundary AdS orbifold and DLCQ holography: A universal holographic description of extremal black hole horizons," arXiv:hep-th/0311237.
51. J. Maldacena and L. Maoz,"Wormholes in AdS," arXiv:hep-th/0401024.
52. E. J. Martinec and W. McElgin,"String theory on AdS orbifolds," JHEP 0204, 029 (2002) [arXiv:hep-th/0106171].
53. E. J. Martinec and W. McElgin,"Exciting AdS orbifolds," JHEP 0210, 050 (2002) [arXiv:hep-th/0206175].
54. G. T. Horowitz and D. Marolf,"A new approach to string cosmology," JHEP 9807, 014 (1998) [arXiv:hep-th/9805207].
55. H. Liu, G. Moore and N. Seiberg,"Strings in a time-dependent orbifold," JHEP 0206, 045 (2002) [arXiv:hep-th/0204168].
56. H. Liu, G. Moore and N. Seiberg,"Strings in time-dependent orbifolds," JHEP 0210, 031 (2002) [arXiv:hep-th/0206182].
57. H. Liu, G. Moore and N. Seiberg,"The challenging cosmic singularity," arXiv:gr-qc/0301001.
58. L. Cornalba and M. S. Costa,"Time-dependent orbifolds and string cosmology," arXiv:hep-th/0310099.
59. G. T. Horowitz and J. Polchinski,"Instability of spacelike and null orbifold singularities," Phys. Rev. D 66, 103512 (2002) [arXiv:hep-th/0206228].
60. P. Kraus, H. Ooguri and S. Shenker,"Inside the horizon with AdS/CFT," Phys. Rev. D 67, 124022 (2003) [arXiv:hep-th/0212277].
61. Y. Petridis and M. Skarsholm Risager,"Modular symbols have a normal distribution," preprint.
62. C. Itzykson, J.-M. Luck, P. Moussa, and M. Waldschmidt, eds. Fro m Number Theory to Physics, Springer Verlag, 1995
63. G. W. Moore,"Arithmetic and attractors," arXiv:hep-th/9807087.
64. H. Iwaniec, Topics in Classical Automorphic Forms, AMS Graduate Studies in Math. 17 1997; Introduction to the Spectral Theory of Auto-morphic Forms, Revista Mathematica Iberoamericana, 1995
65. G. W. Moore,"Attractors and arithmetic," arXiv:hep-th/9807056.
66. S. D. Miller and G. W. Moore,"Landau-Siegel zeroes and black hole entropy," arXiv:hep-th/9903267.
67. M. Lynker, V. Periwal and R. Schimmrigk,"Complex multiplication symmetry of black hole attractors," arXiv:hep-th/0303111.
68. M. Lynker, V. Periwal and R. Schimmrigk,"Black hole attractor varieties and complex multiplication," arXiv:math.ag/0306135.
69. M. Lynker, R. Schimmrigk and S. Stewart,"Complex Multiplication of Exactly Solvable Calabi-Yau Varieties," arXiv:hep-th/0312319.
70. S. Ferrara, R. Kallosh, and A. Strominger,"N=2 Extremal Black Holes," hep-th/9508072
71. A. Strominger,"Macroscopic Entropy of N = 2 Extremal Black Holes," Phys. Lett. B 383, 39 (1996) [arXiv:hep-th/9602111].
72. B. de Wit, P. G. Lauwers and A. Van Proeyen,"Lagrangians Of N=2 Supergravity-Matter Systems," Nucl. Phys. B 255, 569 (1985).
73. L. Andrianopoli, M. Bertolini, A. Ceresole, R. D'Auria, S. Ferrara, P. Fre and T. Magri,"N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map," J. Geom. Phys. 23, 111 (1997) [arXiv:hep-th/9605032].
74. S. Ferrara and R. Kallosh,"Universality of Sypersymmetric Attractors," hep-th/9603090; "Supersymmetry and Attractors," hep-th/9602136; S. Ferrara,"Bertotti-Robinson Geometry and Supersymmetry," hep-th/9701163
75. S. Ferrara, G. W. Gibbons and R. Kallosh,"Black holes and critical points in moduli space," Nucl. Phys. B 500, 75 (1997) [arXiv:hep-th/ 9702103].
76. F. Denef,"Supergravity flows and D-brane stability," JHEP 0008, 050 (2000) [arXiv:hep-th/0005049].
77. F. Denef, B. Greene and M. Raugas,"Split attractor flows and the spectrum of BPS D-branes on the quintic," JHEP 0105, 012 (2001) [arXiv:hep-th/0101135].
78. F. Denef,"Quantum quivers and Hall/hole halos," JHEP 0210, 023 (2002) [arXiv:hep-th/0206072].
79. B. Bates and F. Denef,"Exact solutions for supersymmetric stationary black hole composites," arXiv:hep-th/0304094.
80. T. Shioda and H. Inose,"On singular K3 surfaces," in Complex analysis and algebraic geometry, Cambridge University Press, Cambridge, 1977
81. 2, John Wiley, 1989.
82. J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices, and Groups, Springer Verlag, 1993
83. S. Gukov and C. Vafa,"Rational conformal field theories and complex multiplication," arXiv:hep-th/0203213.
84. A. Connes, Noncommutative Geometry, Academic Press (1994).
85. C. M. Hull and P. K. Townsend,"Unity of superstring dualities," Nucl. Phys. B 438, 109 (1995) [arXiv:hep-th/9410167].
86. R. Kallosh and B. Kol,"E(7) Symmetric Area of the Black Hole Horizon," Phys. Rev. D 53, 5344 (1996) [arXiv:hep-th/9602014].
87. P. Candelas, X. De La Ossa, A. Font, S. Katz and D. R. Morrison,"Mirror symmetry for two parameter models. I," Nucl. Phys. B 416, 481 (1994) [arXiv:hep-th/9308083].
88. N. Yui, 'Update on the modularity of Calabi-Yau varieties," Fields Communication Series Vol. 38 (2003), pp. 307-362. American Math. Soc.
89. C. Vafa,"Evidence for F-Theory," Nucl. Phys. B 469, 403 (1996) [arXiv:hep-th/9602022].
90. P. S. Aspinwall,"K3 surfaces and string duality," arXiv:hep-th/9611137.
91. A. Clingher and J. W. Morgan,"Mathematics underlying the F-theory/heterotic string duality in eight dimensions," arXiv:math.ag/0308106.
92. K. Wendland,"Moduli spaces of unitary conformal field theories," Ph. D. Thesis, University of Bonn, BONN-IR-2000-11
93. K. Wendland,"On Superconformal Field Theories Associated to Very Attractive Quartics," arXiv:hep-th/0307066.
94. S. Hosono, B. H. Lian, K. Oguiso and S. T. Yau,"Classification of c = 2 rational conformal field theories via the Gauss product," arXiv:hep-th/0211230.
95. B. H. Lian and S. T. Yau,"Arithmetic properties of mirror map and quantum coupling," Commun. Math. Phys. 176, 163 (1996) [arXiv:hep-th/ 9411234].
96. R. Friedman, J. Morgan and E. Witten,"Vector bundles and F theory," Commun. Math. Phys. 187, 679 (1997) [arXiv:hep-th/9701162].
97. R. Friedman, J. W. Morgan and E. Witten,"Principal G-bundles over elliptic curves," Math. Res. Lett. 5, 97 (1998) [arXiv:alg-geom/9707004].
98. S. B. Giddings, S. Kachru and J. Polchinski,"Hierarchies from fluxes in string compactifications," Phys. Rev. D 66, 106006 (2002) [arXiv:hep-th/0105097].
99. S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi,"De Sitter vacua in string theory," Phys. Rev. D 68, 046005 (2003) [arXiv:hep-th/0301240].
100. S. Ashok and M. R. Douglas,"Counting Flux Vacua," arXiv:hep-th/0307049.
101. S. Gukov, C. Vafa and E. Witten,"CFT's from Calabi-Yau four-folds," Nucl. Phys. B 584, 69 (2000) [Erratum-ibid. B 608, 477 (2001)] [arXiv:hep-th/9906070].
102. M. Grana and J. Polchinski,"Supersymmetric three-form flux perturbations on AdS(5)," Phys. Rev. D 63, 026001 (2001) [arXiv:hep-th/0009211].
103. K. Becker and M. Becker,"M-Theory on Eight-Manifolds," Nucl. Phys. B 477, 155 (1996) [arXiv:hep-th/9605053].
104. G. Curio, A. Klemm, B. Kors and D. Lust,"Fluxes in heterotic and type II string compactifications," Nucl. Phys. B 620, 237 (2002) [arXiv:hep-th/0106155].
105. G. Curio, A. Klemm, D. Lust and S. Theisen,"On the vacuum structure of type II string compactifications on Calabi-Yau spaces with H-fluxes," Nucl. Phys. B 609, 3 (2001) [arXiv:hep-th/0012213].
106. A. Sen,"Orientifold limit of F-theory vacua," Nucl. Phys. Proc. Suppl. 68, 92 (1998) [Nucl. Phys. Proc. Suppl. 67, 81 (1998)] [arXiv:hep-th/9709159].
107. A. Giryavets, S. Kachru, P. K. Tripathy and S. P. Trivedi,"Flux com-pactifications on Calabi-Yau threefolds," arXiv:hep-th/0312104.
108. P. K. Tripathy and S. P. Trivedi,"Compactification with flux on K3 and tori," JHEP 0303, 028 (2003) [arXiv:hep-th/0301139].
109. S. Kachru, M. B. Schulz and S. Trivedi,"Moduli stabilization from fluxes in a simple IIB orientifold," arXiv:hep-th/0201028.
110. F. Denef and M. Douglas, to appear