Direct integration of the topological string

Journal of High Energy Physics

Volumn 2007, Issue 8, 2007, Pages

  Grimm, Thomas W ^a   Klemm, Albrecht ^a   Mariño, Marcos ^b   Weiss, Marlene ^b,c  

^a Wisconsin Electric Machines and Power Electronics Consortium   (United States)

^b CERN   (Switzerland)

^c ETH ZURICH   (Switzerland)

Author keywords

Differential and algebraic geometry; String duality; Topological strings

Indexed keywords

EID: 77953250224     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/08/058     Document Type: Article

References (67)

1. M. Aganagic, V. Bouchard and A. Klemm, Topological strings and (almost) modular forms, hep-th/0607100.
2. M. Aganagic, A. Klemm, M. Marino and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132].
3. I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, N = 2 type-II heterotic duality and higher derivative f terms, Nucl. Phys. B 455 (1995) 109 [hep-th/9507115].
4. P.S. Aspinwall, An N = 2 dual pair and a phase transition, Nucl. Phys. B 460 (1996) 57 [hep-th/9510142].
5. P.S. Aspinwall, K3 surfaces and string duality, hep-th/9611137.
6. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, Nucl. Phys. B 405 (1993) 279 [hep-th/9302103].
7. 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 [hep-th/9309140].
8. s+2,2(K) and infinite products, Inv. Math. 120 (1995) 161.
9. R.E. Borcherds, The moduli space of Enriques surfaces and the fake monster Lie superalgebra, Topology 35 (1996) 699.
10. R.E. Borcherds, Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998) 491 [alg-geom/9609022].
11. C. Borcea, K3-surfaces with involutions and Mirror pairs of Calabi-Yau manifolds, in Mirror symetry II, B. Greene and S.S. Yau eds., AMS/International Press (1997).
12. U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multi-instanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108].
13. P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455.
14. A. Ceresole, R. D'Auria and S. Ferrara, The symplectic structure of N = 2 supergravity and its central extension, Nucl. Phys. 46 (Proc. Suppl.) (1996) 67 [hep-th/9509160];
15. L. Andrianopoli et al., 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 (1997) 111 [hep-th/9605032].
16. B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special Kahler geometry?, Nucl. Phys. B 503 (1997) 565 [hep-th/9703082].
17. R. Dijkgraaf, Mirror symmetry and elliptic curves and M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms in The Moduli Space of Curves, Prog. Math. 129, Birkhäuser (1995).
18. R. Dijkgraaf, personal communication (1998).
19. R. Dijkgraaf, E.P. Verlinde and M. Vonk, On the partition sum of the ns five-brane, hep-th/0205281.
20. M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102].
21. N. Dorey, V.V. Khoze and M.P. Mattis, Multi-instanton calculus in N = 2 supersymmetric gauge theory. II: coupling to matter, Phys. Rev. D 54 (1996) 7832 [hep-th/9607202],
22. N. Dorey, V.V. Khoze and M.P. Mattis, On N = 2 supersymmetric QCD with A flavors, Nucl. Phys. B 492 (1997) 607 [hep-th/9611016].
23. B. Eynard, M. Marino and N. Orantin, Holomorphic anomaly and matrix models, JHEP 06 (2007) 058 [hep-th/0702110].
24. S. Ferrara, J. A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59 [hep-th/9505162].
25. D.S. Freed, Special Kahler manifolds, Commun. Math. Phys. 203 (1999) 31 [hep-th/9712042].
26. R.W. Gebert, Introduction to vertex algebras, borcherds algebras and the monster Lie algebra, Int. J. Mod. Phys. A 8 (1993) 5441 [hep-th/930815l].
27. R. Gopakumar and C. Vafa, M-theory and topological strings. I, hep-th/9809187;
28. M-theory and topological strings. II, hep-th/9812127.
29. M. Günaydin, A. Neitzke and B. Pioline, Topological wave functions and heat equations, JHEP 12 (2006) 070 [hep-th/0607200].
30. J.A. Harvey and G.W. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182].
31. J.A. Harvey and G.W. Moore, Exact gravitational threshold correction in the FHSV model, Phys. Rev. D 57 (1998) 2329 [hep-th/9611176].
32. K. Hori et al., Mirror symmetry, AMS, Providence (2003).
33. S. Hosono, M.H. Saito and A. Takahashi, Holomorphic anomaly equation and BPS state counting of rational elliptic surface, Adv. Theor. Math. Phys. 3 (1999) 177 [hep-th/990115l].
34. S. Hosono, Counting BPS states via holomorphic anomaly equations, hep-th/0206206.
35. M.-X. Huang and A. Klemm, Holomorphic anomaly in gauge theories and matrix models, hep-th/0605195.
36. M.-X. Huang, A. Klemm and S. Quackenbush, Topological string theory on compact Calabi-Yau: modularity and boundary conditions, hep-th/0612125.
37. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Nonperturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537 [hep-th/9508155].
38. S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239].
39. S.H. Katz, A. Klemm and C. Vafa, M-theory, topological strings and spinning black holes, Adv. Theor. Math. Phys. 3 (1999) 1445 [hep-th/9910181].
40. T. Kawai and K. Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397 [hep-th/0002169].
41. A. Klemm, Topological string theory and integrable structures, Fortschr. Phys. 53 (2005) 720.
42. A. Klemm, M. Kreuzer, E. Riegler and E. Scheidegger, Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections, JHEP 05 (2005) 023 [hep-th/0410018].
43. A. Klemm and M. Mariño, Counting BPS states on the enriques Calabi-Yau, hep-th/0512227.
44. H. Klingen, Introductory lectures on Siegel modular forms, Cambridge University Press (1990).
45. G. Lopes Cardoso, D. Lüst and T. Mohaupt, Threshold corrections and symmetry enhancement in string compactifications, Nucl. Phys. B 450 (1995) 115 [hep-th/9412209]
46. M. Mariño, Chern-Simons theory, matrix models, and topological strings, Oxford University Press (2005).
47. M. Marino, Open string amplitudes and large order behavior in topological string theory, hep-th/0612127.
48. M. Mariño and G.W. Moore, Counting higher genus curves in a Calabi-Yau manifold, Nucl. Phys. B 543 (1999) 592 [hep-th/9808131].
49. D. Maulik, N. Nekrasov, A. Okounkov and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory, I, math.AG/0312059;
50. Gromov-Witten theory and Donalds on-Thomas theory, II, math. AG/0406092.\
51. D. Maulik and R. Pandharipande, New calculations in Gromov-Witten theory, math.AG/0601395.
52. J. A. Minahan, D. Nemeschansky and N.P. Warner, Partition functions for BPS states of the non-critical E(8) string, Adv. Theor. Math. Phys. 1 (1998) 167 [hep-th/9707149]
53. Instanton expansions for mass deformed N = 4 super Yang-Mills theories, Nucl. Phys. B 528 (1998) 109 [hep-th/9710146].
54. J. A. Minahan, D. Nemeschansky, C. Vafa and N.P. Warner, Estrings and N = A topological Yang-Mills theories, Nucl. Phys. B 527 (1998) 581 [hep-th/9802168].
55. A. Neitzke and C. Vafa, Topological strings and their physical applications, hep-th/0410178.
56. N.A. Nekrasov, Seiberg- Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161].
57. N. Nekrasov and A. Okounkov, Seiberg- Witten theory and random partitions, hep-th/0306238.
58. 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 [Erratum ibid. 430 (1994) 485] [hep-th/9407087].
59. N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099].
60. A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995) 96 [hep-th/9504090].
61. G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric, in S.-T. Yau (ed.), Mathematical aspects of string theory, World Scientific, Singapore (1987);
62. A.N. Todorov, The Weil-Petersson geometry of the moduli space of SU(n ≥ 3) (Calabi-Yau) manifolds I, Commun. Math. Phys. 126 (1989) 325.
63. C. Vafa, A stringy test of the fate of the conifold, Nucl. Phys. B 447 (1995) 252 [hep-th/9505023].
64. E.P. Verlinde, Attractors and the holomorphic anomaly, hep-th/0412139.
65. M. Vonk, A mini-course on topological strings, hep-th/0504147.
66. E. Witten, Quantum background independence in string theory, hep-th/9306122.
67. S. Yamaguchi and S.-T. Yau, Topological string partition functions as polynomials, JHEP 07 (2004) 047 [hep-th/0406078].