Seiberg-Witten curve via generalized matrix model

Journal of High Energy Physics

Volumn 2011, Issue 1, 2011, Pages

  Maruyoshi, Kazunobu ^a   Yagi, Futoshi ^b  

^a KYOTO UNIVERSITY   (Japan)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

Brane dynamics in gauge theories; Conformal field models in string theory; M theory; Topological strings

Indexed keywords

EID: 80053096800     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2011)042     Document Type: Article

References (62)

1. 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].
2. E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166].
3. D. Gaiotto, N=2 dualities, arXiv:0904.2715.
4. N. A. Nekrasov, Seiberg-Witten Prepotential From Instanton Counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161].
5. N-1 conformal Toda field theory correlation functions from conformal N = 2 SU (N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189].
6. A. Mironov and A. Morozov, On AGT relation in the case of U (3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569].
7. S. Kanno, Y. Matsuo, S. Shiba and Y. Tachikawa, N=2 gauge theories and degenerate fields of Toda theory, Phys. Rev. D 81 (2010) 046004 [arXiv:0911.4787].
8. S. Kanno, Y. Matsuo and S. Shiba, Analysis of correlation functions in Toda theory and AGT-W relation for SU (3) quiver, Phys. Rev. D 82 (2010) 066009 [arXiv:1007.0601].
9. D. Gaiotto, Asymptotically free N = 2 theories and irregular conformal blocks, arXiv:0908.0307.
10. A. Marshakov, A. Mironov and A. Morozov, On non-conformal limit of the AGT relations, Phys. Lett. B 682 (2009) 125 [arXiv:0909.2052].
11. M. Taki, On AGT Conjecture for Pure Super Yang-Mills and W-algebra, arXiv:0912.4789.
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].
13. N. Drukker, J. Gomis, T. Okuda and J. Teschner, Gauge Theory Loop Operators and Liouville Theory, JHEP 02 (2010) 057 [arXiv:0909.1105].
14. N. Drukker, D. Gaiotto and J. Gomis, The Virtue of Defects in 4D Gauge Theories and 2D CFTs, arXiv:1003.1112.
15. F. Passerini, Gauge Theory Wilson Loops and Conformal Toda Field Theory, JHEP 03 (2010) 125 [arXiv:1003.1151].
16. C. Kozcaz, S. Pasquetti and N. Wyllard, A & B model approaches to surface operators and Toda theories, JHEP 08 (2010) 042 [arXiv:1004.2025].
17. L. F. Alday and Y. Tachikawa, Affine SL (2) conformal blocks from 4d gauge theories, Lett. Math. Phys. 94 (2010) 87 [arXiv:1005.4469].
18. T. Dimofte, S. Gukov and L. Hollands, Vortex Counting and Lagrangian 3-manifolds, arXiv:1006.0977.
19. K. Maruyoshi and M. Taki, Deformed Prepotential, Quantum Integrable System and Liouville Field Theory, Nucl. Phys. B 841 (2010) 388 [arXiv:1006.4505].
20. M. Taki, Surface Operator, Bubbling Calabi-Yau and AGT Relation, arXiv:1007.2524.
21. H. Awata, H. Fuji, H. Kanno, M. Manabe and Y. Yamada, Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String, arXiv:1008.0574.
22. C. Kozcaz, S. Pasquetti, F. Passerini and N. Wyllard, Affine sl (N) conformal blocks from N = 2 SU (N) gauge theories, arXiv:1008.1412.
23. K. Hosomichi, S. Lee and J. Park, AGT on the S-duality Wall, arXiv:1009.0340.
24. T.-S. Tai, Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants, JHEP 10 (2010) 107 [arXiv:1008.4332].
25. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, Phys. Lett. B 691 (2010) 111 [arXiv:0909.4031].
26. L. F. Alday, F. Benini and Y. Tachikawa, Liouville/Toda central charges from M5-branes, Phys. Rev. Lett. 105 (2010) 141601 [arXiv:0909.4776].
27. V. A. Fateev and A. V. Litvinov, On AGT conjecture, JHEP 02 (2010) 014 [arXiv:0912.0504].
28. f = 0, 1, 2 antifundamentals, JHEP 06 (2010) 046 [arXiv:1004.1841].
29. A. B. Zamolodchikov, Conformal Symmetry In Two-Dimensions: An Explicit Recurrence Formula For The Conformal Partial Wave Amplitude, Commun. Math. Phys. 96 (1984) 419.
30. c QCD, JHEP 11 (2009) 048 [arXiv:0909.3338].
31. R. Poghossian, Recursion relations in CFT and N = 2 SYM theory, JHEP 12 (2009) 038 [arXiv:0909.3412].
32. L. Hadasz, Z. Jaskolski and P. Suchanek, Recursive representation of the torus 1-point conformal block, JHEP 01 (2010) 063 [arXiv:0911.2353].
33. R. Dijkgraaf and C. Vafa, Toda Theories, Matrix Models, Topological Strings and N = 2 Gauge Systems, arXiv:0909.2453.
34. V. S. Dotsenko and V. A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys. B 240 (1984) 312.
35. V. S. Dotsenko and V. A. Fateev, Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c ¡ 1, Nucl. Phys. B 251 (1985) 691.
36. A. Marshakov, A. Mironov and A. Morozov, Generalized matrix models as conformal field theories: Discrete case, Phys. Lett. B 265 (1991) 99.
37. S. Kharchev, A. Marshakov, A. Mironov, A. Morozov and S. Pakuliak, Conformal matrix models as an alternative to conventional multimatrix models, Nucl. Phys. B 404 (1993) 717 [hep-th/9208044].
38. H. Itoyama, K. Maruyoshi and T. Oota, The Quiver Matrix Model and 2d-4d Conformal Connection, Prog. Theor. Phys. 123 (2010) 957 [arXiv:0911.4244].
39. T. Eguchi and K. Maruyoshi, Penner Type Matrix Model and Seiberg-Witten Theory, JHEP 02 (2010) 022 [arXiv:0911.4797].
40. R. Schiappa and N. Wyllard, An Ar threesome: Matrix models, 2d CFTs and 4d N = 2 gauge theories, arXiv:0911.5337.
41. T. Eguchi and K. Maruyoshi, Seiberg-Witten theory, matrix model and AGT relation, JHEP 07 (2010) 081 [arXiv:1006.0828].
42. M. Fujita, Y. Hatsuda and T.-S. Tai, Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model, JHEP 03 (2010) 046 [arXiv:0912.2988].
43. A. Mironov, A. Morozov and S. Shakirov, Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions, JHEP 02 (2010) 030 [arXiv:0911.5721].
44. A. Mironov, A. Morozov and S. Shakirov, Conformal blocks as Dotsenko-Fateev Integral Discriminants, Int. J. Mod. Phys. A 25 (2010) 3173 [arXiv:1001.0563].
45. H. Itoyama and T. Oota, Method of Generating q-Expansion Coefficients for Conformal Block and N = 2 Nekrasov Function by beta-Deformed Matrix Model, Nucl. Phys. B 838 (2010) 298 [arXiv:1003.2929].
46. A. Mironov, A. Morozov and A. Morozov, Matrix model version of AGT conjecture and generalized Selberg integrals, Nucl. Phys. B 843 (2011) 534 [arXiv:1003.5752].
47. A. Morozov and S. Shakirov, The matrix model version of AGT conjecture and CIV-DV prepotential, JHEP 08 (2010) 066 [arXiv:1004.2917].
48. A. Morozov and S. Shakirov, From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators, arXiv:1007.4100.
49. H. Itoyama, T. Oota and N. Yonezawa, Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type, Phys. Rev. D 82 (2010) 085031 [arXiv:1008.1861].
50. G. Felder, BRST Approach to Minimal Methods, Nucl. Phys. B 317 (1989) 215.
51. 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].
52. R. Donagi and E. Witten, Supersymmetric Yang-Mills Theory And Integrable Systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101].
53. V. Alba and A. Morozov, Non-conformal limit of AGT relation from the 1-point torus conformal block, arXiv:0911.0363.
54. M. Goulian and M. Li, Correlation functions in Liouville theory, Phys. Rev. Lett. 66 (1991) 2051.
55. E. D'Hoker and D. H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917.
56. E. P. Verlinde and H. L. Verlinde, Multiloop Calculations in Covariant Superstring Theory, Phys. Lett. B 192 (1987) 95.
57. R. Dijkgraaf, E. P. Verlinde and H. L. Verlinde, C = 1 Conformal Field Theories on Riemann Surfaces, Commun. Math. Phys. 115 (1988) 649.
58. J. Ambjørn, L. Chekhov, C. F. Kristjansen and Y. Makeenko, Matrix model calculations beyond the spherical limit, Nucl. Phys. B 404 (1993) 127 [hep-th/9302014].
59. G. Akemann, Higher genus correlators for the Hermitian matrix model with multiple cuts, Nucl. Phys. B 482 (1996) 403 [hep-th/9606004].
60. B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, math-ph/0702045.
61. G. Felder, L. Stevens and A. Varchenko, Elliptic Selberg Integrals and Conformal Blocks, math/0210040.
62. V. P. Spiridonov, Elliptic Hypergeometric Integrals, math/0303205.