Nekrasov functions and exact Bohr-Sommerfeld integrals

Journal of High Energy Physics

Volumn 2010, Issue 4, 2010, Pages

  Mironov, A ^a,b   Morozov, A ^b  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

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

Author keywords

Integrable Hierarchies; Supersymmetric gauge theory; Topological Field Theories

Indexed keywords

EID: 77954900966     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP04(2010)040     Document Type: Article

References (65)

1. N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, arXiv:0908.4052 [SPIRES].
2. L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [SPIRES].
3. N. Wyllard, AN-1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [SPIRES].
4. N. Drukker, D.R. Morrison and T. Okuda, Loop operators and S-duality from curves on Riemann surfaces, JHEP 09 (2009) 031 [arXiv:0907.2593] [SPIRES].
5. A. Marshakov, A. Mironov and A. Morozov, On combinatorial expansions of conformal blocks, arXiv:0907.3946 [SPIRES].
6. D. Gaiotto, Asymptotically free N = 2 theories and irregular conformal blocks, arXiv:0908.0307 [SPIRES].
7. A. Mironov, S. Mironov, A. Morozov and A. Morozov, CFT exercises for the needs of AGT, arXiv:0908.2064 [SPIRES].
8. A. Mironov and A. Morozov, The power of Nekrasov functions, Phys. Lett. B 680 (2009) 188 [arXiv:0908.2190] [SPIRES].
9. A. Mironov and A. Morozov, On AGT relation in the case of U(3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569] [SPIRES].
10. S.M. Iguri and C.A. Núñez, Coulomb integrals and conformal blocks in the AdS3-WZNW model, JHEP 11 (2009) 090 [arXiv:0908.3460] [SPIRES].
11. D.V. Nanopoulos and D. Xie, On crossing symmmetry and modular invariance in conformal field theory and S duality in gauge theory, Phys. Rev. D 80 (2009) 105015 [arXiv:0908.4409] [SPIRES].
12. L.F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa and H. Verlinde, Loop and surface operators in N = 2 gauge theory and Liouville modular geometry, JHEP 01 (2010) 113 [arXiv:0909.0945] [SPIRES].
13. N. Drukker, J. Gomis, T. Okuda and J. Teschner, Gauge theory loop operators and Liouville theory, JHEP 02 (2010) 057 [arXiv:0909.1105] [SPIRES].
14. A. Marshakov, A. Mironov and A. Morozov, On non-conformal limit of the AGT relations, Phys. Lett. B 682 (2009) 125 [arXiv:0909.2052] [SPIRES].
15. R. Dijkgraaf and C. Vafa, Toda theories, matrix models, topological strings and N = 2 gauge systems, arXiv:0909.2453 [SPIRES].
16. A. Marshakov, A. Mironov and A. Morozov, Zamolodchikov asymptotic formula and instanton expansion in N = 2 SUSY Nf = 2Nc QCD, JHEP 11 (2009) 048 [arXiv:0909.3338] [SPIRES].
17. A. Mironov and A. Morozov, Proving AGT relations in the large-c limit, Phys. Lett. B 682 (2009) 118 [arXiv:0909.3531] [SPIRES].
18. R. Poghossian, Recursion relations in CFT and N = 2 SYM theory, JHEP 12 (2009) 038 [arXiv:0909.3412] [SPIRES].
19. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, arXiv:0909.4031 [SPIRES].
20. L.F. Alday, F. Benini and Y. Tachikawa, Liouville/Toda central charges from M5-branes, arXiv:0909.4776 [SPIRES].
21. H. Awata and Y. Yamada, Five-dimensional AGT conjecture and the deformed Virasoro algebra, JHEP 01 (2010) 125 [arXiv:0910.4431] [SPIRES].
22. V. Alba and A. Morozov, Non-conformal limit of AGT relation from the 1-point torus conformal block, arXiv:0911.0363 [SPIRES].
23. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
24. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
25. A. Lossev, N. Nekrasov and S.L. Shatashvili, Testing Seiberg-Witten solution, hep-th/9801061 [SPIRES].
26. A. Morozov, Integrability and matrix models, Phys. Usp. 37 (1994) 1 [hep-th/9303139] [SPIRES].
27. A. Morozov, Matrix models as integrable systems, hep-th/9502091 [SPIRES].
28. A. Morozov, Challenges of matrix models, hep-th/0502010 [SPIRES].
29. A. Mironov, 2 - D gravity and matrix models. 1. 2 - D gravity, Int. J. Mod. Phys. A 9 (1994) 4355 [hep-th/9312212] [SPIRES].
30. A. Mironov, Matrix models of two-dimensional gravity, Phys. Part. Nucl. 33 (2002) 537.
31. A.S. Alexandrov, A. Mironov and A. Morozov, Partition functions of matrix models as the first special functions of string theory. I: finite size Hermitean 1-matrix model, Int. J. Mod. Phys. A 19 (2004) 4127 [Theor. Math. Phys. 142 (2005) 349] [hep-th/0310113] [SPIRES].
32. A.S. Alexandrov, A. Mironov and A. Morozov, Instantons and merons in matrix models, Physica D 235 (2007) 126 [hep-th/0608228] [SPIRES].
33. A.S. Alexandrov, A. Mironov and A. Morozov, M-theory of matrix models, Teor. Mat. Fiz. 150 (2007) 179 [hep-th/0605171] [SPIRES].
34. A. Alexandrov, A. Mironov and A. Morozov, BGWM as second constituent of complex matrix model, JHEP 12 (2009) 053 [arXiv:0906.3305] [SPIRES].
35. A.S. Alexandrov, A. Mironov, A. Morozov and P. Putrov, Partition functions of matrix models as the first special functions of string theory. II. Kontsevich model, Int. J. Mod. Phys. A 24 (2009) 4939 [arXiv:0811.2825] [SPIRES].
36. N. Seiberg and E. Witten, Monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [SPIRES].
37. 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] [SPIRES].
38. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Integrability and Seiberg-Witten exact solution, Phys. Lett. B 355 (1995) 466 [hep-th/9505035] [SPIRES].
39. P.C. Argyres and A.D. Shapere, The Vacuum structure of N = 2 superQCD with classical gauge groups, Nucl. Phys. B 461 (1996) 437 [hep-th/9509175] [SPIRES].
40. J. Sonnenschein, S. Theisen and S. Yankielowicz, On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories, Phys. Lett. B 367 (1996) 145 [hep-th/9510129] [SPIRES].
41. R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [SPIRES].
42. H. Itoyama and A. Morozov, Integrability and Seiberg-Witten theory: curves and periods, Nucl. Phys. B 477 (1996) 855 [hep-th/9511126] [SPIRES].
43. H. Itoyama and A. Morozov, Prepotential and the Seiberg-Witten theory, Nucl. Phys. B 491 (1997) 529 [hep-th/9512161] [SPIRES].
44. H. Itoyama and A. Morozov, Integrability and Seiberg-Witten theory, hep-th/9601168 [SPIRES].
45. A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, N = 2 supersymmetric QCD and integrable spin chains: rational case Nf
46. A.Marshakov, Seiberg-Witten theory and integrable systems, World Scientific, Singapore (1999).
47. A. Gorsky and A. Mironov, Integrable many-body systems and gauge theories, hep-th/0011197 [SPIRES].
48. N.A. Nekrasov and S.L. Shatashvili, Supersymmetric vacua and Bethe ansatz, Nucl. Phys. Proc. Suppl. 192-193 (2009) 91 [arXiv:0901.4744] [SPIRES].
49. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [SPIRES].
50. A. Mironov and A. Morozov, Virasoro constraints for Kontsevich-Hurwitz partition function, JHEP 02 (2009) 024 [arXiv:0807.2843] [SPIRES].
51. A. Mironov, A. Morozov and S. Natanzon, Complete set of cut-and-join operators in Hurwitz-Kontsevich theory, arXiv:0904.4227 [SPIRES].
52. G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Z. Phys. 38 (1926) 518.
53. L. Brillouin, La mécanique ondulatoire de Schrödinger; une méthode générale de resolution par approximations successives, Comptes Rendus 183 (1926) 24.
54. H.A. Kramers, Wellenmechanik und halbzahlige Quantisierung, Z. Phys. 39 (1926) 828.
55. A. Zwaan, Arch. Neerl. des Sciences 12 (1929) 33.
56. J.L. Dunham, The Wentzel-Brillouin-Kramers method of solving the wave equation, Phys. Rev. 41 (1932) 713.
57. A. Klemm, W. Lerche and S. Theisen, Nonperturbative effective actions of N = 2 supersymmetric gauge theories, Int. J. Mod. Phys. A 11 (1996) 1929 [hep-th/9505150] [SPIRES].
58. A. Gerasimov, D. Lebedev and A. Morozov, On possible implications of integrable systems for string theory, Int. J. Mod. Phys. A 6 (1991) 977 [SPIRES].
59. A. Morozov, Integrable systems and double loop algebras in string theory, Sov. J. Nucl. Phys. 52 (1990) 755 [SPIRES].
60. M. Gutzwiller, The quantum mechanical Toda lattice II, Annals Phys. 133 (1981) 304 [SPIRES].
61. M. Gutzwiller, he quantum mechanical Toda lattice, Annals Phys. 124 (1980) 347 [SPIRES].
62. S. Kharchev and D. Lebedev, Integral representation for the eigenfunctions of quantum periodic Toda chain, Lett. Math. Phys. 50 (1999) 53 [hep-th/9910265] [SPIRES].
63. S. Kharchev and D. Lebedev, Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism, J. Phys. A 34 (2001) 2247 [hep-th/0007040] [SPIRES].
64. V.S. Dotsenko and V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys. B 240 (1984) 312 [SPIRES].
65. A. Gerasimov, A. Morozov, M. Olshanetsky, A. Marshakov and S.L. Shatashvili, Wess-Zumino-Witten model as a theory of free fields, Int. J. Mod. Phys. A 5 (1990) 2495 [SPIRES].