Small instantons, little strings and free fermions

From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection

Volumn 1, Issue , 2005, Pages 581-621

  Losev, Andrei S ^a   Marshakov, Andrei V ^a,b   Nekrasov, Nikita A ^c  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^c INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FREE ENERGY; SUPERSYMMETRY;

CONFORMAL FIELD THEORIES; CORRELATION FUNCTION; GAUGE FIELDS; GAUGE THEORY; NON-COMMUTATIVE; PARTITION FUNCTIONS; TODA LATTICE; TWISTED BOUNDARY CONDITIONS;

LATTICE THEORY;

EID: 85014656281     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812775344_0017     Document Type: Chapter

References (103)

1. E. Witten, Nucl. Phys. B 443, 85 (1995) [hep-th/9503124].
2. A. Polyakov, Nucl. Phys. Proc. Suppl. 68, 1 (1998) [hep-th/9711002]; Int. J. Mod. Phys. A 14, 645 (1999) [hep-th/9809057].
3. J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [hep-th/9711200].
4. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 428, 105 (1998) [hep-th/9802109].
5. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998) [hep-th/9802150].
6. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Nucl. Phys. B 459, 537 (1996) [hep-th/9508155].
7. S. Kachru and C. Vafa, Nucl. Phys. B 450, 69 (1995) [hep-th/9505105].
8. A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. P. Warner, Nucl. Phys. B 477, 746 (1996) [hep-th/9604034].
9. S. Katz, A. Klemm and C. Vafa, Nucl. Phys. B 497, 173 (1997) [hep-th/9609239].
10. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Commun. Math. Phys. 165, 311 (1994) [hep-th/9309140].
11. I. Antoniadis, E. Gava, K. S. Narain and T. R. Taylor, Nucl. Phys. B 413, 162 (1994) [hep-th/9307158].
12. C. Vafa, J. Math. Phys. 42, 2798 (2001) [hep-th/0008142].
13. N. Nekrasov, Adv. Theor. Math. Phys. 7, 831 (2004) [hep-th/0206161].
14. A. Losev, G. W. Moore, N. Nekrasov and S. Shatashvili, Nucl. Phys. Proc. Suppl. 46, 130 (1996) [hep-th/9509151].
15. N. Nekrasov, Nucl. Phys. B 531, 323 (1998) [hep-th/9609219].
16. A. E. Lawrence and N. Nekrasov, Nucl. Phys. B 513, 239 (1998) [hep-th/9706025].
17. A. Losev, N. Nekrasov and S. L. Shatashvili, Nucl. Phys. B 534, 549 (1998) [hep-th/9711108]; Testing Seiberg-Witten solution, hep-th/9801061].
18. G. W. Moore, N. Nekrasov and S. Shatashvili, Commun. Math. Phys. 209, 97 (2000) [hep-th/9712241]; Commun. Math. Phys. 209, 77 (2000) [hep-th/9803265].
19. A. Losev, N. Nekrasov and S. L. Shatashvili, The freckled instantons, hep-th/9908204.
20. U. Bruzzo, F. Fucito, J. F. Morales and A. Tanzini, JHEP 0305, 054 (2003) [hep-th/0211108].
21. D. Bellisai, F. Fucito, A. Tanzini and G. Travaglini, Phys. Lett. B 480, 365 (2000) [hep-th/0002110]; JHEP 0007, 017 (2000) [arXiv: hep-th/0003272]. Nucl. Phys. B 611, 205 (2001) [hep-th/0008225].
22. R. Flume and R. Poghossian, Int. J. Mod. Phys. A 18, 2541 (2003) [hep-th/0208176].
23. R. Flume, R. Poghossian and H. Storch, The coefficients of the Seiberg-Witten prepotential as intersection numbers, hep-th/0110240; Mod. Phys. Lett. A 17, 327 (2002) [hep-th/0112211].
24. N. Dorey, T. J. Hollowood, V. V. Khoze and M. P. Mattis, Phys. Rept. 371, 231 (2002) [hep-th/0206063], and references therein].
25. N. Seiberg and E. Witten, Nucl. Phys. B 426, 19 (1994) [Erratum-ibid. B 430, 485 (1994)] [hep-th/9407087]; Nucl. Phys. B 431, 484 (1994) [hep-th/9408099].
26. N. Seiberg, The Power of holomorphy: Exact results in 4-D SUSY field theories, hep-th/9408013.
27. A. Klemm, W. Lerche, S. Yankielowicz and S. Theisen, Phys. Lett. B 344, 169 (1995) [hep-th/9411048].
28. P. C. Argyres and A. E. Faraggi, Phys. Rev. Lett. 74, 3931 (1995) [hep-th/9411057].
29. A. Hanany and Y. Oz, Nucl. Phys. B 452, 283 (1995) [hep-th/9505075].
30. G. Moore and E. Witten, Adv. Theor. Math. Phys. 1, 298 (1998). [hep-th/9709193].
31. A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, Nucl. Phys. B 527, 690 (1998) [hep-th/9802007].
32. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 355, 466 (1995) [hep-th/9505035].
33. A. Marshakov, Seiberg-Witten Theory and Integrable Systems, (World Scientific, Singapore, 1999)
34. H. Braden and I. Krichever (Eds.) Integrability: The Seiberg-Witten and Whitham Equations, (Gordon and Breach, 2000).
35. A. Klemm and E. Zaslow, Local mirror symmetry at higher genus, hep-th/9906046.
36. R. Dijkgraaf, Nucl. Phys. B 493, 588 (1997) [hep-th/9609022].
37. M. R. Douglas, Conformal field theory techniques in large N Yang-Mills theory, hep-th/9311130; Conformal field theory techniques for large N group theory, hepth/9303159.
38. D. J. Gross, Nucl. Phys. B 400, 161 (1993) [hep-th/9212149].
39. D. J. Gross and W. I. Taylor, Nucl. Phys. B 400, 181 (1993) [hep-th/9301068]; Nucl. Phys. B 403, 395 (1993) [hep-th/9303046].
40. A. Gerasimov, A. Levin and A. Marshakov, Nucl. Phys. B 360, 537 (1991).
41. A. Bilal, V. V. Fock and I. I. Kogan, Nucl. Phys. B 359, 635 (1991).
42. N. Seiberg, Phys. Lett. B 388, 753 (1996) [hep-th/9608111].
43. R. Gopakumar and C. Vafa, M-theory and topological strings. I, hep-th/9809187; M-theory and topological strings. II, hep-th/9812127.
44. S. Cecotti and L. Girardello, Phys. Lett. B 110, 39 (1982).
45. A. V. Smilga, Yad. Piz. 43, 215 (1986).
46. S. Sethi and M. Stern, Commun. Math. Phys. 194, 675 (1998) [hep-th/9705046].
47. J. A. Minahan, D. Nemeschansky, C. Vafa and N. P. Warner, Nucl. Phys. B 527, 581 (1998) [hep-th/9802168].
48. T. Eguchi and K. Sakai, JHEP 0205, 058 (2002) [hep-th/0203025]; Seiberg-Witten curve for E-string theory revisited, hep-th/0211213].
49. O. J. Ganor, Compactification of tensionless string theories, hep-th/9607092; Nucl. Phys. B 488, 223 (1997) [hep-th/9608109].
50. L. Baulieu, A. Losev and N. Nekrasov, Nucl. Phys. B 522, 82 (1998) [hep-th/9707174].
51. A. Marshakov and A. Mironov, Nucl. Phys. B 518, 59 (1998) [hep-th/9711156].
52. H. W. Braden, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 448, 195 (1999) [hep-th/9812078]; Nucl. Phys. B 558, 371 (1999) [hep-th/9902205].
53. T. Eguchi and H. Kanno, Nucl. Phys. B 586, 331 (2000) [hep-th/0005008].
54. H. W. Braden and A. Marshakov, Nucl. Phys. B 595, 417 (2001) [hep-th/0009060].
55. H. W. Braden, A. Gorsky, A. Odessky and V. Rubtsov, Nucl. Phys. B 633, 414 (2002) [hep-th/0111066].
56. C. Csaki, J. Erlich, V. V. Khoze, E. Poppitz, Y. Shadmi and Y. Shirman, Phys. Rev. D 65, 085033 (2002) [hep-th/0110188].
57. T. J. Hollowood, JHEP 0303, 039 (2003) [hep-th/0302165].
58. E. Witten, Nucl. Phys. B 460, 335 (1996) [hep-th/9510135].
59. E. Witten, Nucl. Phys. B 500, 3 (1997) [hep-th/9703166].
60. D. E. Diaconescu, M. R. Douglas and J. Gomis, JHEP 9802, 013 (1998) [hep-th/9712230].
61. A. E. Lawrence, N. Nekrasov and C. Vafa, Nucl. Phys. B 533, 199 (1998) [hep-th/9803015].
62. I. Klebanov and N. Nekrasov, Nucl. Phys. B 574, 263 (2000) [hep-th/9911096].
63. J. Polchinski, Int. J. Mod. Phys. A 16, 707 (2001) [hep-th/0011193].
64. A. Connes, M. R. Douglas and A. Schwarz, JHEP 9802, 003 (1998) [hep-th/9711162].
65. N. Seiberg and E. Witten, JHEP 9909, 032 (1999) [hep-th/9908142].
66. A. Connes, Noncommutative geometry (Academic Press, 1994).
67. O. Aharony, M. Berkooz and N. Seiberg, Adv. Theor. Math. Phys. 2, 119 (1998) [hep-th/9712117].
68. O. Aharony, M. Berkooz, S. Kachru, N. Seiberg and E. Silverstein, Adv. Theor. Math. Phys. 1, 148 (1998) [hep-th/9707079].
69. N. Nekrasov and A. Schwarz, Commun. Math. Phys. 198, 689 (1998) [hep-th/9802068].
70. H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, AMS University Lecture Series, 1999, ISBN 0-8218-1956-9.
71. E. Corrigan and P. Goddard, Annals Phys. 154, 253 (1984).
72. N. Nekrasov, Commun. Math. Phys. 241, 143 (2003) [hep-th/0010017]; Lectures on open strings, and noncommutative gauge fields, hep-th/0203109].
73. H. W. Braden and N. A. Nekrasov, Space-time foam from non-commutative instantons, hep-th/9912019.
74. E. Witten, Commun. Math. Phys. 117, 353 (1988).
75. M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld and Y. I. Manin, Phys. Lett. A 65, 185 (1978).
76. J. J. Duistermaat and G.J. Heckman, Invent. Math. 69, 259 (1982).
77. M. Atiyah and R. Bott, Topology 23 No 1, 1 (1984).
78. M. Atiyah and R. Bott, Phil. Trans. Roy. Soc. London A 308, 524 (1982).
79. E. Witten, J. Geom. Phys. 9 (1992) 303 [hep-th/9204083].
80. S. Cordes, G. W. Moore and S. Ramgoolam, Nucl. Phys. Proc. Suppl. 41, 184 (1995) [hep-th/9411210].
81. R. Bott and J. Diff, Geom. 4, 311 (1967).
82. G. Ellingsrud and S.A. Stromme, Invent. Math. 87, 343 (1987).
83. L. Gottche, Math. A. 286, 193 (1990).
84. M. Kontsevich, Enumeration Of Rational Curves Via Torus Actions, hep-th/9405035.
85. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Phys. Lett. B 217, 103 (1989).
86. A. M. Vershik, Hook formulae and related identities, Zapiski sem. LOMI, 172, 3 (1989) (in Russian).
87. S. V. Kerov and A. M. Vershik, Asymptotics of the Plancherel measure of the symmetric group and the limiting shape of the Young diagrams, DAN SSSR, 233,1024(1977), (in Russian).
88. S. V. Kerov, Random Young tableaux, Teor. veroyat. i ee primeneniya, 3, 627 (1986), (in Russian).
89. A. Losev, G. W. Moore and S. L. Shatashvili, Nucl. Phys. B 522, 105 (1998) [hep-th/9707250].
90. N. Seiberg, Phys. Lett. B 408, 98 (1997) [arXiv: hep-th/9705221].
91. A. Okounkov and R. Pandharipande, The equivariant Gromov-Witten theory of P1, math.AG/0207233; Gromov-Witten theory, Hurwitz theory, and completed cycles, math.AG/0204305.
92. S. Kharchev, Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model, hep-th/9810091.
93. K. Ueno, K. Takasaki, Adv. Studies in Pure Math. 4,1 (1984).
94. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238.
95. V. Balasubramanian, P. Kraus and A. E. Lawrence, Phys. Rev. D 59, 046003 (1999) [hep-th/9805171].
96. R. Dijkgraaf and C. Vafa, Nucl. Phys. B 644, 3 (2002) [hep-th/0206255]; Nucl. Phys. B 644, 21 (2002) [hep-th/0207106]; A perturbative window into non-perturbative physics, hep-th/0208048].
97. R. Dijkgraaf, S. Gukov, V. A. Kazakov and C. Vafa, Phys. Rev. D 68, 045007 (2003) [hep-th/0210238].
98. R. Dijkgraaf, M. T. Grisaru, C. S. Lam, C. Vafa and D. Zanon, Phys. Lett. B 573, 138 (2003) [hep-th/0211017].
99. M. Aganagic, A. Klemm, M. Marino and C. Vafa, JHEP 0402, 010 (2004) [hep-th/0211098].
100. R. Dijkgraaf, A. Neitzke and C. Vafa, Large N strong coupling dynamics in nonsupersymmetric orbifold field theories, hep-th/0211194.
101. F. Cachazo, M. R. Douglas, N. Seiberg and E. Witten, JHEP 0212, 071 (2002)[hep-th/0211170].
102. I. Macdonald, Symmetric functions and Hall polynomials (Oxford University Press, 1998).
103. M. Aganagic, M. Marino and C. Vafa, All loop topological string amplitudes from Chern-Simons theory, hep-th/0206164.