Hitchin equation, singularity, and N = 2 superconformal field theories

Journal of High Energy Physics

Volumn 2010, Issue 3, 2010, Pages

  Nanopoulosa, Dimitri ^a,b,c   Xiea, Dan ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

^b HOUSTON ADVANCED RESEARCH CENTER   (United States)

^c BIOMEDICAL RESEARCH FOUNDATION   (Greece)

Author keywords

Brane dynamics in gauge theories; M theory; Supersymmetric gauge theory; Supersymmetry and duality

Indexed keywords

EID: 77954931483     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2010)043     Document Type: Article

References (58)

1. E. Witten, Geometric langlands from six dimensions, arXiv:0905.2720 [SPIRES].
2. P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [SPIRES].
3. D. Gaiotto, N=2 dualities, arXiv:0904.2715 [SPIRES].
4. S. Gukov and E. Witten, Gauge theory, ramification and the geometric Langlands program, hep-th/0612073 [SPIRES].
5. N. Seiberg and E. Witten, Monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485 [hep-th/9407087] [SPIRES].
6. 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].
7. Y. Tachikawa, Six-dimensional DN theory and four-dimensional SO - USp quivers, JHEP 07 (2009) 067 [arXiv:0905.4074] [SPIRES].
8. F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and N = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [SPIRES].
9. K. Maruyoshi, M. Taki, S. Terashima and F. Yagi, New Seiberg dualities from N = 2 dualities, JHEP 09 (2009) 086 [arXiv:0907.2625] [SPIRES].
10. D. Nanopoulos and D. Xie, N = 2SU quiver with USP ends or SU ends with antisymmetric matter, JHEP 08 (2009) 108 [arXiv:0907.1651] [SPIRES].
11. F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, arXiv:0909.1327 [SPIRES].
12. Y. Zhou, A note on Wilson loop in N = 2 Quiver/M theory gravity duality, arXiv:0910.4234 [SPIRES].
13. D. Gaiotto, Surface operators in N = 2 4D gauge theories, arXiv:0911.1316 [SPIRES].
14. 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].
15. 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].
16. 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].
17. N. Drukker, J. Gomis, T. Okuda and J. Teschner, Gauge theory loop operators and Liouville theory, JHEP 02 (2010) 057 [arXiv:0909.1105] [SPIRES].
18. 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].
19. A. Mironov and A. Morozov, Proving AGT relations in the large-c limit, Phys. Lett. B 682 (2009) 118 [arXiv:0909.3531] [SPIRES].
20. R. Poghossian, Recursion relations in CFT and N = 2 SYM theory, JHEP 12 (2009) 038 [arXiv:0909.3412] [SPIRES].
21. 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].
22. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, arXiv:0909.4031 [SPIRES].
23. 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].
24. 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].
25. D. Gaiotto, Asymptotically free N = 2 theories and irregular conformal blocks, arXiv:0908.0307 [SPIRES].
26. D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, arXiv:0904.4466 [SPIRES].
27. R. Dijkgraaf and C. Vafa, Toda theories, matrix models, topological strings and N = 2 gauge systems, arXiv:0909.2453 [SPIRES].
28. A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d topological QFT, arXiv:0910.2225 [SPIRES].
29. H. Awata and Y. Yamada, Five-dimensional AGT conjecture and the deformed Virasoro algebra, JHEP 01 (2010) 125 [arXiv:0910.4431] [SPIRES].
30. A.Mironov and A.Morozov, Nekrasov functions and exact Bohr-Sommerfeld integrals, arXiv:0910.5670 [SPIRES].
31. V. Alba and A. Morozov, Non-conformal limit of AGT relation from the 1-point torus conformal block, arXiv:0911.0363 [SPIRES].
32. A. Marshakov, A. Mironov and A. Morozov, On combinatorial expansions of conformal blocks, arXiv:0907.3946 [SPIRES].
33. A. Mironov and A. Morozov, The power of Nekrasov functions, Phys. Lett. B 680 (2009) 188 [arXiv:0908.2190] [SPIRES].
34. A. Mironov and A. Morozov, On AGT relation in the case of U(3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569] [SPIRES].
35. E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [SPIRES].
36. R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [SPIRES].
37. A. Kapustin, Solution of N = 2 gauge theories via compactification to three dimensions, Nucl. Phys. B 534 (1998) 531 [hep-th/9804069] [SPIRES].
38. N. Seiberg and E. Witten, Gauge dynamics and compactification to three dimensions, hep-th/9607163 [SPIRES].
39. A. Kapustin and S. Sethi, The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 (1998) 571 [hep-th/9804027] [SPIRES].
40. D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [SPIRES].
41. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three- dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [SPIRES].
42. N. Hitchin, The self-duality equation on a Riemann surface, Proc. Lond. Math. Soc. 55 (1987) 59 [SPIRES].
43. N. Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987) 91 [SPIRES].
44. A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, hep-th/0604151 [SPIRES].
45. S. Gukov and E. Witten, Rigid surface operators, arXiv:0804.1561 [SPIRES].
46. E. Witten, Gauge theory and wild ramification, arXiv:0710.0631 [SPIRES].
47. D. Collingwood and W. McGovern, Nilpotent orbits in semisimple lie algebra, VanNostrand Reinhold Math. Series, New York U.S.A. (1993).
48. P.B. Kronheimer, Instantons and the geometry of the nilpotent variety, J. Diff. Geom. 32 (1990) 473 [SPIRES].
49. P. Kronheimer, A hyper-kahlerian structure on coadjoint orbits of a semisimple complex group, J. London Math. Soc. 42 (1990) 193.
50. K.A. Intriligator and N. Seiberg, Mirror symmetry in three dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [SPIRES].
51. E. Brieskorn, Singular elements of semisimple algebraic groups, Actes du Congres International des Mathematiciens, Volume II, (1970) pg. 279.
52. n, Invent. Math. 62 (1981) 503.
53. K. Landsteiner, E. Lopez and D.A. Lowe, N = 2 supersymmetric gauge theories, branes and orientifolds, Nucl. Phys. B 507 (1997) 197 [hep-th/9705199] [SPIRES].
54. A. Brandhuber, J. Sonnenschein, S. Theisen and S. Yankielowicz, M-theory and Seiberg-Witten curves: orthogonal and symplectic groups, Nucl. Phys. B 504 (1997) 175 [hep-th/9705232] [SPIRES].
55. D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, arXiv:0804.2902 [SPIRES].
56. D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, arXiv:0807.3720 [SPIRES].
57. F. Benini, D. Gaiotto, Y. Tachikawa and D. Xie, D4 branes and three dimensional mirror symmetry, to appear.
58. A.G. Kovalev, Nahm's equations and complex adjoint orbits, Q. J. Math. 47 (1996) 41.