Darboux coordinates, Yang-Yang functional, and gauge theory
详细信息 查看全文
- 作者：N. A. Nekrasov (1) (2) (3) (4)
A. A. Rosly (3) (4)
S. L. Shatashvili (3) (5) (6) (7) (8) - 关键词：gauge theory ; supersymmetry ; Hitchin integrable system ; Darboux variable ; quantization
- 刊名：Theoretical and Mathematical Physics
- 出版年：2014
- 出版时间：October 2014
- 年：2014
- 卷：181
- 期：1
- 页码：1206-1234
- 全文大小：727 KB
- 参考文献：1. L. D. Faddeev, “The Bethe Ansatz,-Preprint SFB-288-70, Sonderforschungsbereich 288, Berlin (1993).
2. C. N. Yang and C. P. Yang, / J. Math. Phys., 10, 1115-122 (1969). CrossRef
3. C. N. Yang and C. P. Yang, / Phys. Rev., 150, 321-27 (1966). CrossRef
4. E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, / Theor. Math. Phys., 40, 688-06 (1979). CrossRef
5. M. Jimbo, T. Miwa, and F. Smirnov, / J. Phys. A, 42, 304018 (2009); arXiv:0811.0439v2 [math-ph] (2008). CrossRef
6. G. W. Moore, N. Nekrasov, and S. Shatashvili, / Commun. Math. Phys., 209, 97-21 (2000); arXiv:hep-th/9712241v2 (1998). CrossRef
7. A. A. Gerasimov and S. L. Shatashvili, / Commun. Math. Phys., 277, 323-67 (2008); arXiv:hep-th/0609024v3 (2006). CrossRef
8. A. A. Gerasimov and S. L. Shatashvili, “Two-dimensional gauge theories and quantum integrable systems,-in: / From Hodge Theory to Integrability and TQFT: / tt*-Geometry (Proc. Symp. Pure Math., Vol. 78, R. Y. Donagi and K. Wendland, eds.), Amer. Math. Soc., Providence, R. I. (2008), pp. 239-62; arXiv:0711.1472v1 [hep-th] (2007).
9. E. Witten, / J. Geom. Phys., 9, 303-68 (1992); arXiv:hep-th/9204083v1 (1992). CrossRef
10. A. S. Gorsky and N. Nekrasov, / Theor. Math. Phys., 100, 874-78 (1994). CrossRef
11. A. Gorsky and N. Nekrasov, / Nucl. Phys. B, 436, 582-08 (1995); arXiv:hep-th/9401017v4 (1994). CrossRef
12. A. Gorsky and N. Nekrasov, “Elliptic Calogero-Moser system from two dimensional current algebra,-arXiv:hep-th/9401021v1 (1994).
13. A. Gorsky and N. Nekrasov, / Nucl. Phys. B, 414, 213-38 (1994); arXiv:hep-th/9304047v1 (1993). CrossRef
14. N. A. Nekrasov and S. L. Shatashvili, / Nucl. Phys. B Proc. Suppl., 192-93, 91-12 (2009); arXiv:0901.4744v2 [hep-th] (2009). CrossRef
15. N. Nekrasov and S. Shatashvili, / AIP Conf. Proc., 1134, 154-69 (2009). CrossRef
16. N. A. Nekrasov and S. L. Shatashvili, / Prog. Theor. Phys. Suppl., 177, 105-19 (2009); arXiv:0901.4748v2 [hep-th] (2009). CrossRef
17. N. A. Nekrasov and S. L. Shatashvili, “Quantization of integrable systems and four dimensional gauge theories,-in: / XVIth International Congress on Mathematical Physics (Prague, Czech Republic, 3- August 2009, P. Exne, ed.), World Scientific, Singapore (2010), pp. 265-89; arXiv:0908.4052v1 [hep-th] (2009). CrossRef
18. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, and A. Morozov, / Phys. Lett. B, 355, 466-74 (1995); arXiv:hep-th/9505035v2 (1995). CrossRef
19. E. Martinec and N. Warner, / Nucl. Phys. B, 459, 97-12 (1996); arXiv:hep-th/9509161v2 (1995).- 作者单位：N. A. Nekrasov (1) (2) (3) (4)
A. A. Rosly (3) (4)
S. L. Shatashvili (3) (5) (6) (7) (8)
1. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York, USA
2. Institut des Hautes études Scientifiques, Bures-sur-Yvette, France
3. Institute for Information Transmission Problems, Moscow, Russia
4. Institute for Theoretical and Experimental Physics, Moscow, Russia
5. Hamilton Mathematics Institute, Trinity College, Dublin, Ireland
6. School of Mathematics, Trinity College, Dublin, Ireland
7. Louis Michel Chair, Institut des Hautes études Scientifiques, Bures-sur-Yvette, France
8. Euler International Mathematical Institute, St. Petersburg, Russia- ISSN：1573-9333
- 作者单位：N. A. Nekrasov (1) (2) (3) (4)
文摘
The moduli space of flat SL 2 connections on a punctured Riemann surface Σ with fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates in which the generating function of the variety of SL 2 -opers is identified with the universal part of the effective twisted superpotential of the corresponding four-dimensional N=2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows defining the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group and relating it to the instanton counting of the four-dimensional gauge theories in the rank-one case.