Matrix models for β-ensembles from Nekrasov partition functions

Journal of High Energy Physics

Volumn 2010, Issue 4, 2010, Pages

  Sułkowski, Piotr ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Extended Supersymmetry; Matrix Models; Topological Strings

Indexed keywords

EID: 77954936446     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP04(2010)063     Document Type: Article

References (61)

1. 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].
2. 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].
3. N.A. Nekrasov, Seiberg-Witten Prepotential From Instanton Counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
4. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [SPIRES].
5. H. Nakajima and K. Yoshioka, Instanton counting on blowup. I 4-dimensional pure gauge theory, math/0306198 [SPIRES].
6. H. Nakajima and K. Yoshioka, Instanton counting on blowup. II: K-theoretic partition function, math/0505553 [SPIRES].
7. N. Nekrasov and S. Shadchin, ABCD of instantons, Commun. Math. Phys. 252 (2004) 359 [hep-th/0404225] [SPIRES].
8. R. Dijkgraaf and C. Vafa, Matrix models, topological strings and supersymmetric gauge theories, Nucl. Phys. B 644 (2002) 3 [hep-th/0206255] [SPIRES].
9. R. Dijkgraaf and C. Vafa, A Perturbative Window into Non-Perturbative Physics, hep-th/0208048 [SPIRES].
10. S. Katz, A. Klemm, C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B497 (1997) 173 [hep-th/9609239] [SPIRES].
11. M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, Topological strings and integrable hierarchies, Commun. Math. Phys. 261 (2006) 451 hep-th/0312085 [SPIRES].
12. A. Iqbal and A.-K. Kashani-Poor, SU(N) geometries and topological string amplitudes, Adv. Theor. Math. Phys. 10 (2006) 1 [hep-th/0306032] [SPIRES].
13. T.J. Hollowood, A. Iqbal and C. Vafa, Matrix Models, Geometric Engineering and Elliptic Genera, JHEP 03 (2008) 069 [hep-th/0310272] [SPIRES].
14. A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [SPIRES].
15. H. Awata and H. Kanno, Instanton counting, Macdonald functions and the moduli space of D-branes, JHEP 05 (2005) 039 [hep-th/0502061] [SPIRES].
16. M. Taki, Refined Topological Vertex and Instanton Counting, JHEP 03 (2008) 048 [arXiv:0710.1776] [SPIRES].
17. H. Awata and H. Kanno, Refined BPS state counting from Nekrasov's formula and Macdonald functions, Int. J. Mod. Phys. A 24 (2009) 2253 [arXiv:0805.0191] [SPIRES].
18. R. Dijkgraaf, S. Gukov, V.A. Kazakov and C. Vafa, Perturbative analysis of gauged matrix models, Phys. Rev. D 68 (2003) 045007 [hep-th/0210238] [SPIRES].
19. A. Klemm, M. Mariño and S. Theisen, Gravitational corrections in supersymmetric gauge theory and matrix models, JHEP 03 (2003) 051 [hep-th/0211216] [SPIRES].
20. A. Klemm, M. Marino and M. Rauch, Direct Integration and Non-Perturbative Effects in Matrix Models, arXiv:1002.3846 [SPIRES].
21. A. Klemm and P. Sulkowski, Seiberg-Witten theory and matrix models, Nucl. Phys. B 819 (2009) 400 [arXiv:0810.4944] [SPIRES].
22. P. Sulkowski, Matrix models for 2* theories, Phys. Rev. D 80 (2009) 086006 [arXiv:0904.3064] [SPIRES].
23. 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].
24. R. Dijkgraaf and C. Vafa, Toda Theories, Matrix Models, Topological Strings and N = 2 Gauge Systems, arXiv:0909.2453 [SPIRES].
25. M. Mehta, Random matrices, Pure and Applied Mathematics Series vol. 142, Elsevier B.V., Amsterdam Netherlands (2004).
26. B. Eynard and O. Marchal, Topological expansion of the Bethe ansatz and non- commutative algebraic geometry, JHEP 03 (2009) 094 [arXiv:0809.3367] [SPIRES].
27. L. Chekhov, B. Eynard and O. Marchal, Topological expansion of the Bethe ansatz and quantum algebraic geometry, arXiv:0911.1664 [SPIRES].
28. B. Eynard, All orders asymptotic expansion of large partitions, J. Stat. Mech. (2008) P07023 [arXiv:0804.0381] [SPIRES].
29. G. Borot, B. Eynard, M. Mulase and B. Safnuk, A matrix model for simple Hurwitz numbers and topological recursion, arXiv:0906.1206 [SPIRES].
30. A. Morozov and S. Shakirov, Generation of Matrix Models by W-operators, JHEP 04 (2009) 064 [arXiv:0902.2627] [SPIRES].
31. A. Morozov and S. Shakirov, On Equivalence of two Hurwitz Matrix Models, Mod. Phys. Lett. A 24 (2009) 2659 [arXiv:0906.2573] [SPIRES].
32. B. Eynard, A Matrix model for plane partitions and TASEP, J. Stat. Mech. (2009) P10011 [arXiv:0905.0535] [SPIRES].
33. B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, math-ph/0702045.
34. V. Bouchard, A. Klemm, M. Mariño and S. Pasquetti, Remodeling the B-model, Commun. Math. Phys. 287 (2009) 117 [arXiv:0709.1453] [SPIRES].
35. M.-x. Huang and A. Klemm, Holomorphicity and Modularity in Seiberg-Witten Theories with Matter, arXiv:0902.1325 [SPIRES].
36. D. Gaiotto, N = 2 dualities, arXiv:0904.2715 [SPIRES].
37. 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].
38. A. Mironov and A. Morozov, The Power of Nekrasov Functions, Phys. Lett. B 680 (2009) 188 [arXiv:0908.2190] [SPIRES].
39. A. Mironov and A. Morozov, On AGT relation in the case of U(3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569] [SPIRES].
40. 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].
41. A. Mironov and A. Morozov, Proving AGT relations in the large-c limit, Phys. Lett. B 682 (2009) 118 [arXiv:0909.3531] [SPIRES].
42. 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].
43. N. Drukker, J. Gomis, T. Okuda and J. Teschner, Gauge Theory Loop Operators and Liouville Theory, JHEP 02 (2010) 057 [arXiv:0909.1105] [SPIRES].
44. H. Awata and Y. Yamada, Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra, JHEP 01 (2010) 125 [arXiv:0910.4431] [SPIRES].
45. H. Itoyama, K. Maruyoshi and T. Oota, Notes on the Quiver Matrix Model and 2d-4d Conformal Connection, arXiv:0911.4244 [SPIRES].
46. T. Eguchi and K. Maruyoshi, Penner Type Matrix Model and Seiberg-Witten Theory, JHEP 02 (2010) 022 [arXiv:0911.4797] [SPIRES].
47. R. Schiappa and N. Wyllard, An Ar threesome: Matrix models, 2d CFTs and 4d N = 2 gauge theories, arXiv:0911.5337 [SPIRES].
48. A. Mironov, A. Morozov and S. Shakirov, Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions, JHEP 02 (2010) 030 [arXiv:0911.5721] [SPIRES].
49. 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] [SPIRES].
50. A. Marshakov, A. Mironov and A. Morozov, Generalized matrix models as conformal field theories: Discrete case, Phys. Lett. B 265 (1991) 99 [SPIRES].
51. I. Kostov, Conformal field theory techniques in random matrix models, hep-th/9907060 [SPIRES].
52. R. Dijkgraaf, L. Hollands, P. Sulkowski and C. Vafa, Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions, JHEP 02 (2008) 106 [arXiv:0709.4446] [SPIRES].
53. R. Dijkgraaf, L. Hollands and P. Sulkowski, Quantum Curves and D-Modules, JHEP 11 (2009) 047 [arXiv:0810.4157] [SPIRES].
54. K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [SPIRES].
55. Y. Tachikawa, Five-dimensional Chern-Simons terms and Nekrasov's instanton counting, JHEP 02 (2004) 050 [hep-th/0401184] [SPIRES].
56. P. Sulkowski, Deformed boson-fermion correspondence, Q-bosons and topological strings on the conifold, JHEP 10 (2008) 104 [arXiv:0808.2327] [SPIRES].
57. M. Abramowitz and I. Stegun, Handbook of mathematical functions, Applied Mathematics Series vol.55, Dover Publications, New York U.S.A. (1972).
58. F. Tricomi and A. Erdelyi, The Asymptotic Expansion of a Ratio of Gamma Functions, Pacific J. Math. 1 (1951) 133.
59. G. Gasper, q-Extensions of Erdelyi's Fractional Integral Representations for Hypergeometric Functions and Some Summation Formulas for Double q-Kampe de Feriet Series, Contemporary Mathematics vol.254, AMS, Boston U.S.A. (2000).
60. D. Moak, The q-analogue of Stirling's formula, Rocky Mountain J. Math. 14 (1984) 403.
61. q(x), Journal of Nonlinear Math. Phys. 13 (2006) 479.