Special geometry and automorphic forms

Nuclear Physics B

Volumn 503, Issue 1-2, 1997, Pages 256-276

  Berglund, Per ^a   Henningson, Måns ^b   Wyllard, Niclas ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CERN   (Switzerland)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Automorphic forms; Compactification and four dimensional models; Nonperturbative techniques; Special geometry; Supersymmetry

Indexed keywords

EID: 0031566625     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00396-9     Document Type: Article

References (57)

1. [1] A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rep. 244 (1994) 77, hep-th/9401139.
2. [2] B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53, hep-th/9504006.
3. [3] I. Antoniadis, S. Ferrara, E. Gava, K.S. Narain and T.R. Taylor, Perturbative prepotential and monodromies in N = 2 heterotic superstring, Nucl. Phys. B 447 (1995) 35, hep-th/9504034.
4. [4] I. Antoniadis, S. Ferrara, E. Gava, K.S. Narain and T.R. Taylor, Duality symmetries in N = 2 heterotic superstring, Nucl. Phys. B (Proc. Suppl.) 45BC (1996) 177, hep-th/9510079.
5. [5] V. Kaplunovsky, J. Louis and S. Theisen, Aspects of duality in N = 2 string vacua, Phys. Lett. B 357 (1995) 71, hep-th/9506110.
6. [6] J.A. Harvey and G. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315, hep-th/9510182.
7. s+2,2(ℝ) and infinite products, Invent. Math. 120 (1995) 161; Automorphic forms with singularities on Grassmannians, alg-geom/9609022.
8. s+2,2(ℝ) and infinite products, Invent. Math. 120 (1995) 161; Automorphic forms with singularities on Grassmannians, alg-geom/9609022.
9. [8] M. Henningson and G. Moore, Counting curves with modular forms, Nucl. Phys. B 472 (1996) 518, hep-th/9602154.
10. [9] A. Klemm, W. Lerche and P. Mayr, K3 fibrations and heterotic type II string duality, Phys. Lett. B 357 (1995) 313, hep-th/9506112.
11. [10] B.H. Lian and S.-T. Yau, Mirror maps, modular relations and hypergeometric series 1, hep-th/9507151; Mirror maps, modular relations and hypergeometric series 2, hep-th/9507153.
12. [10] B.H. Lian and S.-T. Yau, Mirror maps, modular relations and hypergeometric series 1, hep-th/9507151; Mirror maps, modular relations and hypergeometric series 2, hep-th/9507153.
13. [11] M. Henningson and G. Moore, Threshold corrections in K(3) × T(2) heterotic string compactifications, Nucl. Phys. B 482 (1996) 187, hep-th/9608145.
14. [12] J.A. Harvey and G. Moore, On the algebras of BPS states, hep-th/9609017.
15. [13] B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity - matter systems, Nucl. Phys. B 255 (1985) 569.
16. [14] J. Bagger and E. Witten, Matter couplings in N = 2 supergravity, Nucl. Phys. B 222 (1983) 1.
17. [15] B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N = 2 supergravity -Yang-Mills models, Nucl. Phys. B 245 (1984) 89.
18. [16] E. Cremmer, C. Kounnas, A. Van Proeyen, J.-P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Vector multiplets coupled to N = 2 supergravity: superhiggs effect, flat potentials and geometric structure, Nucl. Phys. B 250 (1985) 385.
19. [17] N. Seiberg, Observations on the modulispace of superconformal field theories, Nucl. Phys. B 303 (1988) 286.
20. [18] C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four dimensions, hep-th/9507050.
21. [19] S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450 (1995) 69, hep-th/9505105.
22. [20] S. Ferrara, J. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59, hep-th/9505162.
23. [21] P.S. Aspinwall and J. Louis, On the ubiquity of K3 fibrations in string duality, Phys. Lett. B 369 (1996) 233, hep-th/9510234.
24. [22] S.-T. Yau ed., Essays on mirror symmetry (International Press, Hong Kong, 1992); B. Greene and S.-T. Yau, eds., Mirror symmetry II (International Press, Hong Kong, 1997).
25. [22] S.-T. Yau ed., Essays on mirror symmetry (International Press, Hong Kong, 1992); B. Greene and S.-T. Yau, eds., Mirror symmetry II (International Press, Hong Kong, 1997).
26. [23] A. Strominger and E. Witten, New manifolds for superstring compactification, Comm. Math. Phys. 101 (1985) 341.
27. [24] M. Dine, N. Seiberg, X.G. Wen and E. Witten, Non-perturbative effects on the string world sheet, Nucl. Phys. B 278 (1986) 769; Non-perturbative effects on the string world sheet 2, Nucl. Phys. B 289 (1987) 319.
28. [24] M. Dine, N. Seiberg, X.G. Wen and E. Witten, Non-perturbative effects on the string world sheet, Nucl. Phys. B 278 (1986) 769; Non-perturbative effects on the string world sheet 2, Nucl. Phys. B 289 (1987) 319.
29. [25] P.S. Aspinwall and D.R. Morrison, Topological field theory and rational curves, Commun. Math. Phys. 151 (1993) 245, hep-th/9110048.
30. [26] A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163.
31. [27] B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special Kähler geometry?, hep-th/9703082.
32. [28] K.S. Narain, New heterotic string theories in uncompactified dimensions < 10, Phys. Lett. B 169 (1986) 41;
33. K.S. Narain, M.H. Sarmadi and E. Witten, A note on toroidal compactification of heterotic string theory, Nucl. Phys. B 279 (1987) 369.
34. [29] S. Ferrara and A. Van Proeyen, A theorem on N = 2 special Kähler product manifolds, Class. Quant. Grav. 6 (1989) L243.
35. [30] M. Dine, P. Huet and N. Seiberg, Large and small radius in string theory, Nucl. Phys. B 322 (1989) 301.
36. [31] K. Oguiso, On algebraic fiber space structures on a Calabi-Yau 3-fold, Int. J. Math. 4 (1993) 439.
37. [32] E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85, hep-th/9503124.
38. [33] P.S. Aspinwall, Enhanced gauge symmetries and K3 surfaces, Phys. Lett. B 357 (1995) 329, hep-th/9507012; Enhanced gauge symmetries and Calabi-Yau threefolds, Phys. Lett. B 371 (1996) 231, hep-th/9511171.
39. [33] P.S. Aspinwall, Enhanced gauge symmetries and K3 surfaces, Phys. Lett. B 357 (1995) 329, hep-th/9507012; Enhanced gauge symmetries and Calabi-Yau threefolds, Phys. Lett. B 371 (1996) 231, hep-th/9511171.
40. [34] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087; Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
41. [34] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087; Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
42. [35] S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155.
43. [36] A. Ceresole, R. D'Auria, S. Ferrara and A. Van Proeyen, Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity, Nucl. Phys. B 444 (1995) 92, hep-th/9502072.
44. [37] P. Candelas, X. de la Ossa, A. Font, S. Katz and D.R. Morrison Mirror symmetry for two parameter models - 1, Nucl. Phys. B 416 (1994) 481, hep-th/9308083.
45. [38] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys. B 433 (1995) 501, hep-th/9406055; Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Commun. Math. Phys. 167 (1995) 301, hep-th/9308122.
46. [38] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys. B 433 (1995) 501, hep-th/9406055; Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Commun. Math. Phys. 167 (1995) 301, hep-th/9308122.
47. [39] G. Aldazabal, L.E. Ibanez, A. Font and F. Quevedo, Chains of N = 2, D = 4 heterotic/type II duals, Nucl. Phys. B 461 (1996) 85, hep-th/9510093.
48. [40] M.J. Duff, R. Minasian and E. Witten, Evidence for Heterotic/Heterotic Duality, Nucl. Phys. B 465 (1996) 413, hep-th/9601036.
49. [41] D.R. Morrison and C. Vafa, Compactifications of F-Theory on Calabi-Yau threefolds - I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Compactifications of F-Theory on Calabi-Yau threefolds - II, Nucl. Phys. B 476 (1996) 437, hep-th/9603161
50. [41] D.R. Morrison and C. Vafa, Compactifications of F-Theory on Calabi-Yau threefolds - I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Compactifications of F-Theory on Calabi-Yau threefolds - II, Nucl. Phys. B 476 (1996) 437, hep-th/9603161
51. [42] E. Witten, Phase Transitions in M-Theory and F-Theory, Nucl. Phys. B 471 (1996) 195, hep-th/9603150.
52. [43] V.A. Gritsenko and V.V. Nikulin, The Igusa modular forms and 'the simplest' Lorentzian Kac-Moody algebras, alg-geom/9603010.
53. [44] G.L. Cardoso, G. Curio and D. Lüst, Perturbative couplings and modular forms in N = 2 string models with a Wilson line, hep-th/9608154.
54. [45] G.L. Cardoso, Perturbative gravitational couplings and Siegel modular forms in D = 4, N = 2 string models, hep-th/9612200.
55. [46] J.-I. Igusa, On Siegel modular forms of genus two, Am. J. Math. 84 (1962) 175; On Siegel modular forms of genus two (II), Am. J. Math. 86 (1964) 392; Modular forms and projective invariants, Am. J. Math. 89 (1967) 817.
56. [46] J.-I. Igusa, On Siegel modular forms of genus two, Am. J. Math. 84 (1962) 175; On Siegel modular forms of genus two (II), Am. J. Math. 86 (1964) 392; Modular forms and projective invariants, Am. J. Math. 89 (1967) 817.
57. [46] J.-I. Igusa, On Siegel modular forms of genus two, Am. J. Math. 84 (1962) 175; On Siegel modular forms of genus two (II), Am. J. Math. 86 (1964) 392; Modular forms and projective invariants, Am. J. Math. 89 (1967) 817.