Exceptional string: Instanton expansions and Seiberg-Witten curve

Reviews in Mathematical Physics

Volumn 14, Issue 9, 2002, Pages 913-975

  Mohri, Kenji ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

E string; Local mirror symmetry; Seiberg Witten curve

Indexed keywords

EID: 0036755558     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X02001466     Document Type: Article

References (41)

1. 8 instantons and tensionless non-critical strings, Nucl. Phys. B474 (1996) 122-138.
2. O.J. Ganor, Toroidal compactification of heterotic 6D non-critical strings down to four dimensions, Nucl. Phys. B488 (1997) 223-235.
3. 8 theory, Nucl. Phys. B487 (1997) 93-127.
4. A. Klemm, P. Mayr and C. Vafa, BPS states of exceptional non-critical strings, Nucl. Phys. B (Proc. Suppl.) 58 (1997) 177-194.
5. W. Lerche, P. Mayr and N.P. Warner, Non-critical strings, del Pezzo singularities and Seiberg-Witten curves, Nucl. Phys. B499 (1997) 125-148.
6. 8 string, Adv. Theor. Math, Phys. 1 (1998) 167-183.
7. J.A. Minahan, D. Nemeschansky, C. Vafa and N.P. Warner, E-strings and N = 4 topological Yang-Mills theories, Nucl. Phys. B527 (1998) 581-623.
8. S. Hosono, M.-H. Salto and J. Stienstra, On the mirror symmetry conjecture for Schoen's Calabi-Yau 3-folds, in Integrable System and Algebraic Geometry, Proc. Taniguchi Symposium 1997, eds. M.-H. Saito, Y. Shimizu and K. Ueno, World Scientific, 1998, pp. 194-235.
9. 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) 177-208.
10. T.-M. Chiang, A. Klemm, S.-T. Yau and E. Zaslow, Local mirror symmetry: calculations and interpretations, Adv. Theor. Math. Phys. 3 (1999) 495-565.
11. S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys. B433 (1995) 501-552.
12. R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z. 193 (1986) 537-558.
13. O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Uncovering infinite symmetries on [p, q] 7-branes: Kac-Moody algebras and beyond, Adv. Theor. Math. Phys. 3 (1999) 1835-1891.
14. K. Saito, Extended affine root systems II (flat invariants), Publ. RIMS, Kyoto Univ. 20 (1990) 15-78.
15. I. Satake, Automorphisms of the extended affine root systems and modular property for the flat theta invariants, Publ. RIMS, Kyoto Univ. 31 (1995) 1-32.
16. 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) 311-427.
17. T. Kawai and K. Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397-485.
18. A.N. Schellekens and N.P. Warner, Anomalies, characters and strings, Nucl. Phys. B287 (1987) 317-361.
19. G. Curio and D. Lüst, A class of N = 1 dual string pairs and its modular superpotentials, Int. J. Mod. Phys. 12 (1997) 5847-5866.
20. M. Fukae, Y. Yamada and S.-K. Yang, Mordell-Weil lattice via string junctions, Nucl. Phys. B572 (2000) 71-94.
21. S. Hosono, M.-H. Saito and A. Takahashi, Relative Lefschetz action and BPS state counting, Int. Math. Res. Notice. 15 (2001) 783-816.
22. B. Schoeneberg, Elliptic Modular Functions: An Introduction, Die Grundlehren der mathematischen Wissenschaften, Bd. 203, Springer-Verlag, 1974.
23. K. Mohri, Y. Ohtake and S.-K. Yang, Dualities between string junctions and D-branes on del Pezzo surfaces, Nucl. Phys. B595 (2001) 138-164.
24. K. Mohri, Y. Onjo and S.-K. Yang, Closed sub-monodromy problems, local mirror symmetry and branes on orbifolds, Rev. Math. Phys. 13(6) (2001) 675-715.
25. G. Aldazabal, A. Font, L.E. Ibáñez and A.M. Uranga, New branches of string compactifications and their F-theory duals, Nucl. Phys. B492 (1996) 119-151.
26. B.H. Lian and S.-T. Yau, Arithmetic properties of mirror map and quantum coupling, Commun. Math. Phys. 176 (1996) 163-191.
27. P. Candelas, X.C. de la Ossa, P.S. Green and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B359 (1991) 21-74.
28. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, Nucl. Phys. B405 (1993) 279-304.
29. R. Gopakurnar and C. Vafa, M-theory and topological strings II, preprint.
30. J. Bryan and R. Pandharipande, BPS states of curves in Calabi-Yau 3-folds, Geometry and Topology 5 (2001) 287-318.
31. S. Katz, A. Klemm and C. Vafa, M-theory, topological strings and spinning black holes, Adv. Theor. Math. Phys. 3 (1999) 1445-1537.
32. K. Wirthmüller, Root systems and Jacobi forms, Compositio Math. 82 (1992) 293-354.
33. N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B431 (1994) 484-550.
34. T. Hauer and A. Iqbal, Del Pezzo surfaces and affine 7-brane backgrounds, J. High Energy Phys. 0001 (2000) 043.
35. E. Looijenga, Rational surfaces with an anti-canonical cycle, Ann. Math. 114 (1981) 267-322.
36. H. Sakai, Rational surfaces with affine root systems and geometry of the Painlevé equations, Commun. Math. Phys. 220 (2001) 165-221.
37. A. Hurwitz und R. Courant, Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen, Die Grundlehren der mathematischen Wissenschaften, Bd. 3, Springer-Verlag, 1929.
38. J. Tannery et J. Molk, Éléments de la Théorie des Fonctions Elliptiques, Tomes I-IV, Gauthier-Villars, 1893-1902; reprinted in two vols. Chelsea, New York, 1972.
39. D. Hilbert, Theory of Algebraic Invariants, Cambridge Mathematical Library, Cambridge Univ. Press, 1993.
40. B. Sturmfels, Algorithms in Invariant Theory, Texts and Monographs in Symbolic Computation, Springer, 1993.
41. n strings, Nucl. Phys. B508 (1997) 64-106.