Relating gauge theories via Gauge/Bethe correspondence

Journal of High Energy Physics

Volumn 2010, Issue 10, 2010, Pages

  Orlando, Domenico ^a   Reffert, Susanne ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Bethe ansatz; Field theories in lower dimensions; Intersecting branes models; Superstring vacua

Indexed keywords

EID: 78649687508     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP10(2010)071     Document Type: Article

References (35)

1. E. J. Martinec and N. P. Warner, Integrable systems and supersymmetric gauge theory, Nucl. Phys. B 459 (1996) 97 [hep-th/9509161].
2. R. Donagi and E. Witten, Supersymmetric Yang-Mills Theory And Integrable Systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101].
3. c, Phys. Lett. B 380 (1996) 75 [hep-th/9603140].
4. A. Gorsky, S. Gukov and A. Mironov, Multiscale N = 2 SUSY field theories, integrable systems and their stringy/brane origin. I, Nucl. Phys. B 517 (1998) 409 [hep-th/9707120].
5. A. Gorsky, S. Gukov and A. Mironov, SUSY field theories, integrable systems and their stringy/brane origin. II, Nucl. Phys. B 518 (1998) 689 [hep-th/9710239].
6. R. Boels and J. de Boer, Classical spin chains and exact three-dimensional superpotentials, Nucl. Phys. B 715 (2005) 234 [hep-th/0411110].
7. L. D. Faddeev and G. P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [hep-th/9404173].
8. J. A. Minahan and K. Zarembo, The Bethe-ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208].
9. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251].
10. R. Dijkgraaf, D. Orlando and S. Reffert, Dimer models, free fermions and super quantum mechanics, arXiv:0705.1645.
11. R. Dijkgraaf, D. Orlando and S. Reffert, Quantum Crystals and Spin Chains, Nucl. Phys. B 811 (2009) 463 [arXiv:0803.1927].
12. R. Dijkgraaf, D. Orlando and S. Reffert, Relating Field Theories via Stochastic Quantization, Nucl. Phys. B 824 (2010) 365 [arXiv:0903.0732].
13. N. A. Nekrasov and S. L. Shatashvili, Supersymmetric vacua and Bethe ansatz, Nucl. Phys. Proc. Suppl. 192-193 (2009) 91 [arXiv:0901.4744].
14. N. A. Nekrasov and S. L. Shatashvili, Quantum integrability and supersymmetric vacua, Prog. Theor. Phys. Suppl. 177 (2009) 105 [arXiv:0901.4748].
15. N. A. Nekrasov and S. L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories, arXiv:0908.4052.
16. N. Nekrasov and E. Witten, The Omega Deformation, Branes, Integrability and Liouville Theory, JHEP 09 (2010) 092 [arXiv:1002.0888].
17. 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].
18. R. Dijkgraaf and C. Vafa, Toda Theories, Matrix Models, Topological Strings and N = 2 Gauge Systems, arXiv:0909.2453.
19. K. Hori et al., Clay Mathematics Monographs. Vol. 1: Mirror Symmetry, American Mathematical Society, Cambridge MA U. S. A. (2003).
20. E. Witten, Phases of N = 2 theories in two dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042].
21. A. Hanany and K. Hori, Branes and N = 2 theories in two dimensions, Nucl. Phys. B 513 (1998) 119 [hep-th/9707192].
22. L. D. Faddeev, How Algebraic Bethe Ansatz works for integrable model, hep-th/9605187.
23. P. P. Kulish and N. Y. Reshetikhin, Diagonalisation of GL (N) invariant transfer matrices and quantum N-wave system (Lee model), J. Phys. A 16 (1983) 591.
24. V. Kazakov, A. S. Sorin and A. Zabrodin, Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics, Nucl. Phys. B 790 (2008) 345 [hep-th/0703147].
25. N. Y. Reshetikhin, The spectrum of the transfer matrices connected with kac-moody algebras, Lett. Math. Phys. 14 (1987) 235.
26. C.-N. Yang and C. P. Yang, Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction, J. Math. Phys. 10 (1969) 1115.
27. V. V. Bazhanov, T. Lukowski, C. Meneghelli and M. Staudacher, A Shortcut to the Q-Operator, arXiv:1005.3261.
28. F. C. Zhang and T. M. Rice, Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37 (1988) 3759.
29. F. H. L. Essler and V. E. Korepin, Higher conservation laws and algebraic Bethe ansatze for the supersymmetric t-J model, Phys. Rev. B 46 (1992) 9147.
30. P.-A. Bares, J. M. P. Carmelo, J. Ferrer and P. Horsch, Charge-spin recombination in the one-dimensional supersymmetric t-J model, Phys. Rev. B 46 (1992) 14624.
31. A. Foerster and M. Karowski, Completeness of the bethe states for the supersymmetric t-j model, Phys. Rev. B 46 (1992) 9234.
32. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230].
33. J. H. Brodie, Two dimensional mirror symmetry from M-theory, Nucl. Phys. B 517 (1998) 36 [hep-th/9709228].
34. V. G. Kac, A Sketch of Lie Superalgebra Theory, Commun. Math. Phys. 53 (1977) 31.
35. V. G. Kac, Lie Superalgebras, Adv. Math. 26 (1977) 8.