Vertices, vortices & interacting surface operators

Journal of High Energy Physics

Volumn 2012, Issue 6, 2012, Pages

  Bonelli, Giulio ^a   Tanzini, Alessandro ^a   Zhao, Jian ^a  

^a SEZIONE DI TRIESTE   (Italy)

Author keywords

Conformal and W symmetry; Nonperturbative Effects; Supersymmetric gauge theory; Topological strings

Indexed keywords

EID: 84864193731     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP06(2012)178     Document Type: Article

References (63)

1. M. Aganagic, A. Klemm and C. Vafa, Disk instantons, mirror symmetry and the duality web, Z. Naturforsch. A 57 (2002) 1 [hep-th/0105045].
2. M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132].
3. M. Aganagic, R. Dijkgraaf, A. Klemm, M. Mariño and C. Vafa, Topological strings and integrable hierarchies, Commun. Math. Phys. 261 (2006) 451 [hep-th/0312085].
4. 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].
5. 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].
6. L.F. Alday and Y. Tachikawa, Affine SL(2) conformal blocks from 4D gauge theories, Lett. Math. Phys. 94 (2010) 87 [arXiv:1005.4469].
7. A. Braverman, B. Feigin, M. Finkelberg and L. Rybnikov, A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces, Commun. Math. Phys. 308 (2011) 457 [arXiv:1008.3655].
8. H. Awata and Y. Yamada, Five-dimensional AGT conjecture and the deformed Virasoro algebra, JHEP 01 (2010) 125 [arXiv:0910.4431].
9. J. Baptista, Non-Abelian vortices on compact Riemann surfaces, Commun. Math. Phys. 291 (2009) 799 [arXiv:0810.3220].
10. A. Belavin, A.M. Polyakov and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333.
11. I. Biswas and N.M. Romao, Moduli of vortices and Grassmann manifolds, arXiv:1012.4023.
12. A. Brini, Open topological strings and integrable hierarchies: remodeling the A-model, Commun. Math. Phys. 312 (2012) 735 [arXiv:1102.0281].
13. A. Brini, M. Mariño and S. Stevan, The uses of the refined matrix model recursion, J. Math. Phys. 52 (2011) 052305 [arXiv:1010.1210].
14. A. Marshakov, A. Mironov and A. Morozov, On AGT relations with surface operator insertion and stationary limit of beta-ensembles, J. Geom. Phys. 61 (2011) 1203
15. [Teor. Mat. Fiz. 164 (2010) 1] [arXiv:1011.4491].
16. M. Taki, Surface operator, bubbling Calabi-Yau and AGT relation, JHEP 07 (2011) 047 [arXiv:1007.2524].
17. D. Gaiotto, Surface operators in N = 2 4D gauge theories, arXiv:0911.1316.
18. 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.
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. U. Bruzzo et al., D-branes, surface operators and ADHM quiver representations, arXiv:1012.1826.
21. A. Mironov and A. Morozov, Nekrasov functions from exact BS periods: the case of SU(N), J. Phys. A 43 (2010) 195401 [arXiv:0911.2396].
22. A. Mironov and A. Morozov, Nekrasov functions and exact Bohr-Zommerfeld integrals, JHEP 04 (2010) 040 [arXiv:0910.5670].
23. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, Phys. Lett. B 691 (2010) 111 [arXiv:0909.4031].
24. J. Teschner, Quantization of the Hitchin moduli spaces, Liouville theory and the geometric Langlands correspondence I, arXiv:1005.2846.
25. U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multiinstanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108].
26. N. Caporaso, L. Griguolo, M. Mariño, S. Pasquetti and D. Seminara, Phase transitions, double-scaling limit and topological strings, Phys. Rev. D 75 (2007) 046004 [hep-th/0606120].
27. M.C. Cheng, R. Dijkgraaf and C. Vafa, Non-perturbative topological strings and conformal blocks, JHEP 09 (2011) 022 [arXiv:1010.4573].
28. R. Dijkgraaf and C. Vafa, Toda theories, matrix models, topological strings and N = 2 gauge systems, arXiv:0909.2453.
29. K. Maruyoshi and F. Yagi, Seiberg-Witten curve via generalized matrix model, JHEP 01 (2011) 042 [arXiv:1009.5553].
30. G. Bonelli, K. Maruyoshi, A. Tanzini and F. Yagi, Generalized matrix models and AGT correspondence at all genera, JHEP 07 (2011) 055 [arXiv:1011.5417].
31. T. Dimofte, S. Gukov and L. Hollands, Vortex counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977].
32. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Moduli space of non-Abelian vortices, Phys. Rev. Lett. 96 (2006) 161601 [hep-th/0511088].
33. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Solitons in the Higgs phase: the moduli matrix approach, J. Phys. A 39 (2006) R315 [hep-th/0602170].
34. V. Fateev and A. Litvinov, Correlation functions in conformal Toda field theory. I, JHEP 11 (2007) 002 [arXiv:0709.3806].
35. V.A. Fateev, A. Litvinov, A. Neveu and E. Onofri, Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks, J. Phys. A 42 (2009) 304011 [arXiv:0902.1331].
36. R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176].
37. F. Fucito, J.F. Morales, R. Poghossian and A. Tanzini, N = 1 superpotentials from multi-instanton calculus, JHEP 01 (2006) 031 [hep-th/0510173].
38. D. Gaiotto, N = 2 dualities, arXiv:0904.2715.
39. A.A. Gerasimov and D.R. Lebedev, On topological field theory representation of higher analogs of classical special functions, JHEP 09 (2011) 076 [arXiv:1011.0403].
40. A. Givental, A mirror theorem for toric complete intersections, in Topological field theory, primitive forms and related topics, Kyoto Japan (1996) [Progr. Math. 160 (1998) 141] [alg-geom/9701016].
41. A. Givental and Y.-P. Lee, Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups, math.AG/0108105.
42. A. Hanany and K. Hori, Branes and N = 2 theories in two-dimensions, Nucl. Phys. B 513 (1998) 119 [hep-th/9707192].
43. A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150].
44. R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Non-Abelian superconductors: vortices and confinement in N = 2 SQCD, Nucl. Phys. B 673 (2003) 187 [hep-th/0307287].
45. M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149].
46. A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158].
47. T. Fujimori, T. Kimura, M. Nitta and K. Ohashi, Vortex counting from field theory, JHEP 06 (2012) 028 [arXiv:1204.1968].
48. A. Iqbal and A.-K. Kashani-Poor, The vertex on a strip, Adv. Theor. Math. Phys. 10 (2006) 317 [hep-th/0410174].
49. S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of Quantum Field Theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239].
50. C. Kozcaz, S. Pasquetti and N. Wyllard, A & B model approaches to surface operators and Toda theories, JHEP 08 (2010) 042 [arXiv:1004.2025].
51. A. Mironov and A. Morozov, The power of Nekrasov functions, Phys. Lett. B 680 (2009) 188 [arXiv:0908.2190].
52. A. Mironov and A. Morozov, On AGT relation in the case of U(3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569].
53. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161].
54. N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, arXiv:0908.4052.
55. R. Poghossian, Deforming SW curve, JHEP 04 (2011) 033 [arXiv:1006.4822].
56. R. Santachiara and A. Tanzini, Moore-Read fractional quantum Hall wavefunctions and SU(2) quiver gauge theories, Phys. Rev. D 82 (2010) 126006 [arXiv:1002.5017].
57. S. Shadchin, On F-term contribution to effective action, JHEP 08 (2007) 052 [hep-th/0611278].
58. E. Witten, Topological s-models, Commun. Math. Phys. 118 (1988) 411.
59. E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166].
60. E. Witten, Surface operators in gauge theory, Fortsch. Phys. 55 (2007) 545.
61. S. Gukov and E. Witten, Rigid surface operators, arXiv:0804.1561.
62. -1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189].
63. Y. Yoshida, Localization of vortex partition functions in N = (2, 2) super Yang-Mills theory, arXiv:1101.0872.