Topological strings and (almost) modular forms

Communications in Mathematical Physics

Volumn 277, Issue 3, 2008, Pages 771-819

  Aganagic, Mina ^a   Bouchard, Vincent ^b   Klemm, Albrecht ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

^c University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37449025111     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0383-3     Document Type: Article

References (43)

1. Aganagic M., Dijkgraaf R., Klemm A., Mariño M. and Vafa C. (2006). Topological strings and integrable hierarchies. Commun. Math. Phys. 261: 451
2. Aganagic M., Klemm A., Mariño M. and Vafa C. (2004). Matrix model as a mirror of Chern-Simons theory. JHEP 0402: 010
3. Aganagic M., Klemm A., Mariño M. and Vafa C. (2005). The topological vertex. Commun. Math. Phys. 254: 425
4. Aganagic M., Mariño M. and Vafa C. (2004). All loop topological string amplitudes from Chern-Simons theory. Commun. Math. Phys. 247: 467
5. Bershadsky M., Cecotti S., Ooguri H. and Vafa C. (1993). Holomorphic anomalies in topological field theories. Nucl. Phys. B 405: 279
6. Bershadsky M., Cecotti S., Ooguri H. and Vafa C. (1994). Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Commun. Math. Phys. 165: 311
7. Bryan, J. et al.: Work in progress
8. Candelas P., DeLa Ossa X.C., Green P.S. and Parkes L. (1991). A Pair Of Calabi-Yau Manifolds As An Exactly Soluble Superconformal Theory. Nucl. Phys. B 359: 21
9. Cassels J.W.S. (1991). Lectures on Elliptic Curves, London Mathematical Society Student Texts 24. Cambridge University Press, Cambridge
10. Chiang T.M., Klemm A., Yau S.T. and Zaslow E. (1999). Local mirror symmetry: Calculations and interpretations. Adv. Theor. Math. Phys. 3: 495
11. Connell, I.: Elliptic curve handbook, Montreal: McGill University, 1996, available at http://www.math.mcgill.ca/connell/public/ECH1/,1996
12. de Wit, B.: N = 2 electric-magnetic duality in a chiral background. Nucl. Phys. Proc. Suppl. 49, 191 (1996);
13. de Wit, B.: N, =,2 symplectic reparametrizations in a chiral background. Fortsch. Phys. 44, 529 (1996);
14. de Wit, B., Lopes Cardoso, G., Lust, D., Mohaupt, T., Rey, S.J.: Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications. Nucl. Phys. B 481, 353 (1996)
15. Dijkgraaf, R.: Mirror symmetry and elliptic curves. In: The moduli space of curves (Texel Island, 1994), Boston MA: Birkhuser Boston, 1995, pp. 149-163
16. Dijkgraaf R., Gukov S., Neitzke A. and Vafa C. (2005). Topological M-theory as unification of form theories of gravity. Adv. Theor. Math. Phys. 9: 593
17. Dijkgraaf, R., Verlinde, E.P., Vonk, M.: On the partition sum of the NS five-brane. http://arXiv.org/list/hepth/0205281, 2002
18. Douglas, M.R., Moore, G.W.: D-branes, Quivers, and ALE Instantons. http://arXiv.org/list/hepth/9603167, 1996
19. Farkas H. and Kra I. (2001). Theta Constants, Riemann Surfaces and the Modular Group. Amer. Math. Soc, Providence, RI
20. Gerasimov A.A. and Shatashvili S.L. (2004). Towards integrability of topological strings. I: Three-forms on Calabi-Yau manifolds. JHEP 0411: 074
21. Ghitza, A.: An elementary introduction to Siegel modular forms. Talk given at the Number Theory Seminar, University of Illinois at Urbana-Champaign, http://www.math.mcgill.ca/∼ghitza/uiuc-siegel1.pdf
22. Hori, K., Vafa, C.: Mirror symmetry. arXiv:hepth/0002222
23. Huang, M.X., Klemm, A.: Holomorphic anomaly in gauge theories and matrix models. http://arXiv.org/list/hepth/0605195, 2006
24. Kachru S., Klemm A., Lerche W., Mayr P. and Vafa C. (1996). Nonperturbative results on the point particle limit of N = 2 heterotic string compactifications. Nucl. Phys. B 459: 537
25. Kaneko, M., Zagier, D.B.: A generalized Jacobi theta function and quasimodular forms. In: The moduli space of curves. Progr. Math. 129, Boston, MA:Birkhauser, 1995, pp. 165-172
26. Katz S., Klemm A. and Vafa C. (1997). Geometric engineering of quantum field theories. Nucl. Phys. B 497: 173
27. Klemm A., Lerche W. and Theisen S. (1996). Nonperturbative effective actions of N = 2 supersymmetric gauge theories. Int. J. Mod. Phys. A 11: 1929
28. Klemm A., Mariño M. and Theisen S. (2003). Gravitational corrections in supersymmetric gauge theory and matrix models. JHEP 0303: 051
29. Klemm, A., Zaslow, E.: Local mirror symmetry at higher genus. http://arXiv.org/list/hepth/9906046, 1999
30. Klingen H. (1990). Introductory lectures on Siegel modular forms. Vol. 20 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge
31. Mariño, M., Moore, G.W.: The Donaldson-Witten function for gauge groups of rank larger than one. Commun. Math. Phys. 199, 25 (1998);
32. Mariño, M.: The uses of Whitham hierarchies. Prog. Theor. Phys. Suppl. 135, 29 (1999)
33. Moore G.W. and Witten E. (1998). Integration over the u-plane in Donaldson theory. Adv. Theor. Math. Phys. 1: 298
34. Nekrasov N.A. (2004). Seiberg-Witten prepotential from instanton counting. Adv. Theor. Math. Phys. 7: 831
35. Nekrasov, N., Okounkov, A.: Seiberg-Witten theory and random partitions. http://arXiv.org/list/hepth/0306238, 2003
36. Nekrasov N. (2005). Z-theory: Chasing M-F-Theory. Comptes Rendus Physique 6: 261
37. Ruan, Y.-B. et al.: Work in progress
38. Seiberg, N., Witten, E.: Electric - magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory. Nucl. Phys. B 426, 19 (1994) [Erratum-ibid. B 430, 485 (1994)]
39. Seiberg N. and Witten E. (1994). Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD. Nucl. Phys. B 431: 484
40. Vafa C. (1989). Quantum Symmetries Of String Vacua. Mod. Phys. Lett. A 4: 1615
41. Vafa C. and Witten E. (1995). On orbifolds with discrete torsion. J. Geom. Phys. 15: 189
42. Verlinde, E.P.: Attractors and the holomorphic anomaly. http://arXiv.org/list/hepth/0412139, 2004
43. Witten, E.: Quantum background independence in string theory. http://arXiv.org/list/hepth/9306122, 1993