On integrable systems and supersymmetric gauge theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 3-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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The properties of the $\mathcal N=2$ SUSY gauge theories underlying the Seiberg–Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated. Recently found exact nonperturbative solutions to $\mathcal N=2$ SUSY gauge theories are formulated using the methods of the theory of integrable systems and where it is possible the parallels between standard quantum field theory results and solutions to integrable systems are discussed.
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A. V. Marshakov. On integrable systems and supersymmetric gauge theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 3-46. http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a0/

[1] A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, A. Morozov, Phys. Lett. B, 355 (1995), 466 ; E-print hep-th/9505035 | DOI | MR | Zbl

[2] E. Martinec, N. Warner, E-print hep-th/9509161

[3] T. Nakatsu, K. Takasaki, E-print hep-th/9509162

[4] R. Donagi, E. Witten, E-print hep-th/9510101

[5] E. Martinec, E-print hep-th/9510204

[6] A. Gorsky, A. Marshakov, ; Phys. Lett. B, 375 (1996), 127 E-print hep-th/9510224 | DOI | MR | Zbl

[7] E. Martinec, N. Warner, E-print hep-th/9511052

[8] H. Itoyama, A. Morozov, E-print hep-th/9511126

[9] A. Marshakov, Mod. Phys. Lett. A, 11 (1996), 1169 ; E-print hep-th/9602005 | DOI | MR | Zbl

[10] C. Ann, S. Nam, E-print hep-th/9603028

[11] A. Gorsky, A. Marshakov, A. Mironov, A. Morozov, ; Phys. Lett. B, 380 (1996), 75 E-print hep-th/9603140 | DOI | MR

[12] A. Gorsky, A. Marshakov, A. Mironov, A. Morozov, ; Problems in Modern Theoretical Physics, Dubna, 1996, 44–62 E-print hep-th/9604078

[13] I. Krichever, D. Phong, E-print hep-th/9604199

[14] A. Marshakov, Preprint FIAN/TD-11/96

[15] A. Marshakov, Preprint FIAN/TD-16/96

[16] A. Marshakov, A. Mironov, A. Morozov, Preprint FIAN/TD-10/96

[17] A. Marshakov, A. Mironov, A. Morozov, Preprint FIAN/TD-15/96

[18] A. Marshakov, A. Mironov, A. Morozov, Preprint FIAN/TD-01/97

[19] N. Nekrasov, E-print hep-th/9609219

[20] N. Seiberg, E. Witten, Nucl. Phys. B, 426 (1994), 19 ; E-print hep-th/9407087 | DOI | MR | Zbl

[21] N. Seiberg, E. Witten, Nucl. Phys. B, 431 (1994), 484 ; E-print hep-th/9408099 | DOI | MR | Zbl

[22] A. Klemm, W. Lerche, S. Theisen, S. Yankielowicz, Phys. Lett. B, 344 (1995), 169 ; ; P. Argyres, A. Faraggi, Phys. Rev. Lett., 73 (1995), 3931 ; E-print hep-th/9411048E-print hep-th/9411057 | DOI | MR | DOI | MR

[23] A. Hanany, Y. Oz, E-print hep-th/9505075

[24] K. Vilson, Dzh. Kogut, Renormalizatsionnaya gruppa i $\varepsilon$-razlozhenie, Mir, M., 1975

[25] K. Ueno, K. Takasaki, Adv. Studies in Pure Math., 4, 1984, 1 | MR | Zbl

[26] M. Sato, RIMS, 439 (1981), 30 ; M. Sato, Y. Sato, Lect. Not. Num. Appl. Anal., 5 (1982), 259; Non-linear partial differential equations in applied science, North Holland, Amsterdam–New York, 1983, 259 | Zbl | Zbl

[27] G. Segal, G. Wilson, Publ. I H. E. S., 61 (1985), 1

[28] I. M. Krichever, Funkts. analiz i ego prilozh., 11 (1977), 15 | Zbl

[29] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov, Nauka, M., 1980 | MR

[30] B. A. Dubrovin, UMN, 36:2 (1981), 11 | MR

[31] B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “Integriruemye sistemy, I”, Dinamicheskie sistemy–4, Sovrem. probl. matematiki, VINITI, M., 1985, 179

[32] I. M. Krichever, UMN, 36:2 (1981), 12 | MR

[33] L. D. Faddeev, L. A. Takhtadzhyan, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR

[34] E. Sklyanin, J. Sov. Math., 47 (1989), 2473 ; Е. К. Склянин, Функц. анализ и его прилож., 16 (1982), 27 ; 17 (1983), 34 | DOI | MR | Zbl | MR | Zbl | MR | Zbl

[35] I. M. Krichever, Funkts. analiz i ego prilozh., 14:4 (1980), 45–54 | MR | Zbl

[36] E. K. Sklyanin, Algebra i analiz, 6:2 (1994), 227 ; H. Braden, T. Suzuki, Lett. Math. Phys., 30 (1994), 147 ; B. Enriquez, V. Rubtsov, ; N. Nekrasov, ; G. Arutyunov, P. Medvedev, E-print alg-geom/9503010E-print hep-th/9503157E-print hep-th/9511070 | MR | Zbl | DOI | MR | Zbl

[37] V. Inozemtsev, Commun. Math. Phys., 121 (1989), 629 | DOI | MR | Zbl

[38] S. Kharchev, A. Marshakov, String Theory, Quantum Gravity, and the Unification of Fundamental Interactions, World Scientific, Singapore, 1993, 331 | MR

[39] S. Kharchev, A. Marshakov, Int. J Mod. Phys. A, 10 (1995), 1219 | DOI | MR | Zbl

[40] I. M. Krichever, UMN, 44:2 (1989), 121 | MR | Zbl

[41] N. Hitchin, Duke. Math. J, 54 (1987), 91 | DOI | MR | Zbl

[42] J. Fay, Theta-functions on Riemann surfaces, Lect. Notes Math., 352, Springer, N. Y., 1973 | DOI | MR | Zbl

[43] D. Mamford, Lektsii o teta-funktsiyakh, Mir, M., 1988 | MR

[44] A. Beilinson, Yu. Manin, Commun. Math. Phys., 107 (1986), 359 | DOI | MR

[45] I. Krichever, Commun. Pure Appl. Math., 47 (1994), 437 ; Preprint LPTENS-92-18 | DOI | MR | Zbl

[46] I. M. Krichever, Funkts. analiz i ego prilozh., 22 (1988), 37 ; I. Krichever, Commun. Math. Phys., 143 (1991), 415 | MR | Zbl | DOI | MR

[47] B. A. Dubrovin, S. P. Novikov, UMN, 44:6 (1989), 29 | MR | Zbl

[48] A. I. Gurevich, L. P. Pitaevskii, ZhETF, 65 (1973), 590 ; В. Е. Захаров, С. В. Манаков, С. П. Новиков, Л. П. Питаевский, Теория солитонов, Наука, М., 1980 | MR | Zbl

[49] B. Dubrovin, ; Nucl. Phys. B, 379 (1992), 627 E-print hep-th/9407018 | DOI | MR

[50] Yu. Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Preprint MPI, 1996 | MR

[51] E. Witten, Surv. Diff. Geom., 1 (1991), 243 | DOI | MR

[52] M. Kontsevich, Yu. Manin, Commun. Math. Phys., 164 (1994), 525 | DOI | MR | Zbl

[53] A. Losev, TMF, 95 (1993), 307 ; A. Losev, I. Polyubin, Int. J Mod. Phys. A, 10 (1995), 4161 | MR | Zbl | DOI | MR | Zbl

[54] W. Lerche, C. Vafa, N. Warner, Nucl. Phys. B, 324 (1989), 427 | DOI | MR

[55] P. Griffits, Dzh. Kharris, Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR

[56] N. Dorey, V. Khoze, M. Mattis, E-print hep-th/9607202

[57] S. Ruijsenaars, “Finite-dimensional Soliton Systems”, Integrable and Super-Integrable Systems, World Scientific, Singapore, 1989 | MR

[58] I. Krichever, E-print hep-th/9611158

[59] E. Markman, Comp. Math., 93 (1994), 255 ; R. Donagi, E. Markman, Cubics, integrable systems, Calabi–Yau Threefolds, preprint ; Spectral covers, algebraically completely integrable Hamiltonian systems, moduli of bundles, preprint | MR | Zbl | MR

[60] N. Seiberg, E. Witten, E-print hep-th/9609219

[61] J. Harvey, G. Moore, E-print hep-th/9510182