On the integrable geometry of soliton equations and n=2 supersymmetric gauge theories

Journal of Differential Geometry

Volumn 45, Issue 2, 1997, Pages 349-389

  Krichever, I M ^a,b   Phong, K D H ^a,b  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031063206     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214459802     Document Type: Article

References (42)

1. N. Seiberg &E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nuclear Phys. B 426 (1994) 19, hepth/9407087;
2. Monopoles, duality, and chiral symmetry breaking in N=2 supersymmetric QCD, Nuclear Phys. B 431 (1994) 484, hepth/9408099.
3. A. Klemm, W. Lerche, S. Yankielowicz &S. Theisen, Simple singularities and N=2 supersymmetric Yang-Mills theory, Phys. Lett. 344 B (1995) 169;
4. P. C. Argyres &A. E Faraggi, The vacuum structure and spectrum of N=2 supersymmetric SU(N) gauge theory, Phys. Rev. Lett. 73 (1995) 3931, hepth/9411057;
5. M. R. Douglas &S. Shenker, Dynamics of SU(N) supersymmetric gauge theory, hepth/9503163;
6. P. C. Argyres &M. R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, hepth/9505062.
7. A. Hanany &Y. Oz, On the guantum moduli space of vacua of N=2 supersymmetric SU(N) gauge theories, hepth/9505075
8. P. Argyres, R. Plesser &A. Shapere, The Coulomb phase of N=2 supersym-metnc QCD, Phys. Rev. Lett. 75 (1995) 1699-1702, hepth/9505100
9. J. Minahan &D. Nemeshansky, Hyperelliptic curves for supersymmetric Yang-Mills, hepth/9507032
10. P. C. Argyres &A. Shapere, The vacuum structure of N=2 super-QCD with classical gauge groups, hepth/9509175
11. A. Hanany, On the guantum moduli space of vacua of N=2 supersymmetric gauge theories, hepth/9509176.
12. U. H. Danielsson &B. Sundborg, Exceptional Eguivalences in N=2 Supersymmetric Yang-Mills Theory, USITP-95-12, UUITP-20/95
13. U. H. Danielsson &B. Sundborg, The moduli space and monodromies of N=2 supersymmetric SO(2r+l) Yang-Mills theory, hepth/9504102;
14. A. Brandhuber &K. Landsteiner, On the monodromies of N=2 supersymmetric Yang-Mills theory with gauge group SO(2n), hepth/9507008
15. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov &A. Morozov, Integrability and Seiberg-Witten exact solutions, Phys. Lett. B 355 (1995) 466, hepth/9505035;
16. E. Martinec &N. Warner, Integrable systems and supersymmetric gauge theory, hepth/9509161, hepth/9511052
17. A. Gorsky &A. Marshakov, Towards effective topological theories on spectral curves, hepth/9510224
18. T. Nakatsu &K. Takasaki, Whitham-Toda hierarchy and N=2 supersymmetric Yang-Mills theory, hepth/9509162
19. H. Itoyama &A. Morozov, Prepotential and the Seiberg- Witten theory, hepth/9511126, hepth/9512161, hepth/9601168
20. A. Marshakov, Exact solutions to quantum field theories and integrable equations, hepth/9602005
21. T. Donagi &E. Witten, Supersymmetric Yang-Mills theory and integrable systems, hepth/950101;
22. E. Martinec, Integrable structures in supersymmetric gauge and string theory, hepth/9510204
23. I. Flaschka, M. G. Forest &D. W. McLaughlin, Multiphase averaging and the inverse spectral solution of the KdV equation, Comm. Pure Appl. Math. 33 (1980) 739-784;
24. B. A. Dubrovin &S. P. Novikov, The Hamiltonian formalism for ID systems of hydrodynamic type and the Bogolyubov-Whitham averaging method, Soviet Math. Dokl. 2 (1983) 665-669;
25. I. M. Krichever, The dispersionless Lax equation and topological minimal models, Comm. Math. Phys. 143 (1992) 415-429;
26. B. A. Dubrovin, Hamiltonian formalism of Whitham hierarchies and topological Landau-Ginzburg models, Comm. Math. Phys. 145 (1992) 195-207.
27. B. A. Dubrovin, Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles, Functional Anal. Appl. 14 (1980) 282-290.
28. B. A. Dubrovin, The averaging method for 2D systems, Functional Anal. Appl. 22 (1988) 200-212.
29. B. A. Dubrovin, The r-function of the universal Whitham hierarchy, matrix models, and topological field theories, Comm. Pure Appl. Math. 47 (1994) 437-475.
30. c, hepth/9603140
31. I. M. Krichever, Methods of algebraic geometry in the theory of non-linear equations, Russian Math. Surveys 32 (1977) 185-213.
32. S. P. Novikov &A. Veselov, On Poisson brackets compatible with algebraic geometry and Korteweg-de Vries dynamics on the space of finite-zone potentials, Soviet Math. Dokl. 26 (1982) 357-362;
33. Poisson brackets and complex tori, Proc. Steklov Inst. Math. 165 (1985) 53-65.
34. S. P. Novikov, S. V. Manakov, L. P. Pitaevski &V. E. Zakharov, Theory of Solitons, Contemp. Soviet Math., Plenum Press, 1984, New York;
35. H. Flaschka &D. McLaughlin, Canonically conjugate variables for KdV and the Toda lattice with periodic boundary conditions, Prog. Theoret. Phys. 55 (1976) 438-456.
36. I. M. Gelfand &L. A. Dickey, Fractional powers of operators and Hamiltonian systems, Functional Anal. Appl. 10 (1976) 13-29;
37. L. A. Dickey, Soliton equations and Hamiltonian systems, World Scientific, 1991, Singapore.
38. I. M. Krichever, The periodic nonabelian Toda lattice and its two-dimensional generalization, Uspekhi Mat. Nauk 36 (1981) 72-77.
39. F. Calogero, A method to generate soluble non-linear evolution eguations, Lett. Nuovo Cimento 14 (1975) 443-447;
40. J. Moser, Three integrable Hamiltonian systems connected with isospectral deformations, Adv. Math. 16 (1975) 197-220;
41. A. M. Perelomov, Completely integrable classical systems connected with semisimple Lie algebras, Lett. Math. Phys. 1 (1977) 531-540.
42. A. Gorsky &N. Nekrasov, Elliptic Calogero-Moser system from two-dimensional current algebra, hepth/9401021