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Strings, SUSY gauge theories, and integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 179-243 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider supersymmetric Yang–Mills theories in the general framework of string theory (M-theory) and describe particular compactifications leading to the Seiberg–Witten (SW) exact effective theories. We show strong parallels between SW and integrable system theories. 
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A. V. Marshakov. Strings, SUSY gauge theories, and integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 179-243. http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a0/

[1] M. Grin, Dzh. Shvarts, E. Vitten, Teoriya superstrun, t. 1, 2, Mir, M., 1990 | MR

[2] R. Dijkgraaf, E. Verlinde, H. Verlinde, Commun. Math. Phys., 115 (1988), 649 | DOI | MR | Zbl

[3] J. Polchinski, Phys. Rev. Lett., 75 (1995), 4724 ; ; Progr. Theor. Phys. Suppl., 123 (1996), 9 ; ; Rev. Mod. Phys., 68 (1996), 1245 ; ; TASI lectures on D-branes, E-print hep-th/9510017E-print hep-th/9511157E-print hep-th/9607050E-print hep-th/9611050 | DOI | MR | Zbl | MR | DOI | MR | DOI

[4] P. Townsend, Phys. Lett. B, 350 (1995), 184 ; ; E. Witten, Nucl. Phys. B, 443 (1995), 85 ; ; P. Townsend, Four lectures on M-theory, ; J. Schwarz, Lectures on superstring and M-theory dualities, ; C. Vafa, Lectures on strings and dualities, E-print hep-th/9501068E-print hep-th/9503124E-print hep-th/9612121E-print hep-th/9607201E-print hep-th/9702201 | DOI | MR | MR | DOI | Zbl

[5] E. Witten, Vector bundles and F-theory, E-print hep-th/9703166

[6] E. Witten, Nucl. Phys. B, 460 (1996), 335 ; E-print hep-th/9510135 | DOI | MR | Zbl

[7] D.-E. Diaconescu, D-branes, monopoles, and Nahm equations, E-print hep-th/9608163 | MR

[8] A. Hanany, E. Witten, Nucl. Phys. B, 492 (1997), 152 ; E-print hep-th/9611230 | DOI | MR

[9] R. Donagi, E. Witten, Nucl. Phys. B, 460 (1996), 299 ; ; E. Martinec, Phys. Lett. B, 367 (1996), 91 ; ; A. Gorsky, A. Marshakov, Phys. Lett. B, 375 (1996), 127 ; ; H. Itoyama, A. Morozov, Nucl. Phys. B, 477 (1996), 855 ; ; E. D'Hoker, D. Phong, Calogero–Moser systems in $SU(N)$ Seiberg–Witten theory, ; Spectral curves for super–Yang–Mills with adjoint hypermultiplet for general Lie algebras, E-print hep-th/9510101E-print hep-th/9510204E-print hep-th/9510224E-print hep-th/9511125E-print hep-th/9709053E-print hep-th/9804126 | DOI | MR | Zbl | MR | DOI | MR | MR | DOI | Zbl | DOI | Zbl | MR

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

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

[12] 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 | MR | DOI

[13] K. Wilson, J. Kogut, “The renormalization group and the $\epsilon$-expansion”, Phys. Rep. C, 12 (1974), 75 | DOI

[14] M. Shifman, A. Vainshtein, Nucl. Phys. B, 277 (1986), 456 | DOI

[15] N. Seiberg, The power of holomorphy – exact results in 4D SUSY field theory, E-print hep-th/9408013 | MR

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

[17] V. Zakharov, S. Manakov, S. Novikov, L. Pitaevskii, Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[18] B. Dubrovin, UMN, 36:2 (1981), 12 | MR

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

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

[21] D. Mumford, Tata Lectures on Theta, v. I, 1983 ; v. II, Birkhäuser, Boston–Basel–Stuttgart, 1984 | MR | Zbl

[22] B. Dubrovin, I. Krichever, S. Novikov, “Integriruemye sistemy, I”, Dinamicheskie sistemy – IV, Itogi nauki i tekhniki. Sovr. probl. matem., ed. R. V. Gamkrelidze, VINITI, M., 1985, 179 | MR

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

[24] A. Gorsky, N. Nekrasov, Elliptic Calogero–Moser system from two dimensional current algebra, E-print hep-th/9401021

[25] N. Nekrasov, Holomorphic bundles and many-body systems, E-print hep-th/9503157 | MR

[26] A. Levin, M. Olshanetsky, Painlevé–Calogero correspondence, E-print alg-geom/9706010 | MR

[27] A. Marshakov, “Seiberg–Witten theory, integrable systems and D-branes”, New Developments in Quantum Field Theory, NATO ASI Series B: Physics, 366, eds. P. H. Damgaard, J. Jurkiewicz, Plenum Press, N. Y., 1999, 279 ; E-print hep-th/9709001 | DOI | MR

[28] A. Gurevich, L. Pitaevskii, ZhETF, 65 (1973), 590

[29] H. Flaschka, D. McLaughlin, Progr. Theor. Phys., 55 (1976), 438 | DOI | MR | Zbl

[30] H. Flaschka, M. Forest, D. McLaughlin, Commun. Pure. Appl. Math., 33 (1980), 739 | DOI | MR | Zbl

[31] I. Krichever, Funct. Anal. Appl., 22 (1988), 37 ; Commun. Math. Phys., 143 (1991), 415 | MR | Zbl | DOI | MR

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

[33] I. Krichever, Commun. Pure Appl. Math., 47 (1994), 437 ; The tau function of the universal Whitham hierarchy, matrix models, and topological field theories, Preprint LPTENS-92-18, Ecole Normale Superiore, Paris, 1992 | DOI | MR | Zbl

[34] B. Dubrovin, Geometry of 2d topological field theory, ; Nucl. Phys. B, 379 (1992), 627 E-print hep-th/9407018 | MR | DOI | MR

[35] H. Itoyama, A. Morozov, Nucl. Phys. B, 491 (1997), 529 ; E-print hep-th/9512161 | DOI | MR | Zbl

[36] A. Gorsky, A. Marshakov, A. Mironov, A. Morozov, Nucl. Phys. B, 527 (1998), 690 ; E-print hep-th/9802007 | DOI | MR | Zbl

[37] A. Marshakov, M. Martellini, A. Morozov, Phys. Lett. B, 418 (1998), 294 ; E-print hep-th/9706050 | DOI | MR

[38] A. Marshakov, TMF, 112 (1997), 3 ; E-print hep-th/9702187 | DOI | MR | Zbl

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

[40] I. Krichever, Funkts. analiz i ego prilozh., 14 (1980), 45 | MR | Zbl

[41] E. Witten, Branes and the dynamics of QCD, E-print hep-th/9706109 | MR

[42] G. Korchemsky, I. Krichever, Solitons in high-energy QCD, E-print hep-th/9704079

[43] H. Braden, A. Marshakov, A. Mironov, A. Morozov, E-print hep-th/9812078

[44] I. Affleck, J. Harvey, E. Witten, Nucl. Phys. B, 206 (1982), 413 | DOI | MR

[45] N. Seiberg, E. Witten, Gauge dynamics and compactification to three dimensions, E-print hep-th/9607163 | MR

[46] S. Katz, C. Vafa, Geometric engineering of $N=1$ quantum field theory, E-print hep-th/9611090 | MR

[47] M. Davies, T. Hollowood, V. Khoze, M. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics, E-print hep-th/9905015 | MR

[48] K. Li, Nucl. Phys. B, 354 (1991), 711 ; 725 ; T. Eguchi, S.-K. Yang, Mod. Phys. Lett. A, 5 (1990), 1693 ; C. Vafa, Mod. Phys. Lett. A, 6 (1991), 337 ; E. Witten, Mirror manifolds and topological field theory, E-print hep-th/9112056 | DOI | MR | MR | DOI | MR | Zbl | DOI | Zbl | MR

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

[50] S. Cecotti, C. Vafa, Phys. Rev. Lett., 68 (1992), 903 ; ; Comm. Math. Phys., 157 (1993), 139 ; ; Comm. Math. Phys., 158 (1993), 569 ; E-print hep-th/9111016E-print hep-th/9209085E-print hep-th/9211097 | DOI | MR | Zbl | MR | DOI | MR | Zbl | DOI | Zbl

[51] A. Marshakov, A. Mironov, A. Morozov, Phys. Lett. B, 389 (1996), 43 ; E-print hep-th/9607109 | DOI | MR

[52] E. Witten, Commun. Math. Phys., 118 (1988), 411 | DOI | MR | Zbl

[53] M. Kontsevich, Yu. Manin, Commun. Math. Phys., 164 (1994), 525 ; ; M. Kontsevich, Enumeration of rational curves via torus actions, ; Homological algebra of mirror symmetry, ; M. Kontsevich, Yu. Manin, Quantum cohomology of a product, , with Appendix by R. Kaufmann ; M. Kontsevich, Yu. Manin, Relations between the correlators of the topological sigma-model coupled to gravity, E-print hep-th/9402147E-print hep-th/9405035E-print alg-geom/9411018E-print q-alg/9502009E-print alg-geom/9708024 | DOI | MR | Zbl | MR | MR | MR

[54] A. Givental, B. Kim, Commun. Math. Phys., 168 (1995), 609 ; ; A. Givental, Equivariant Gromov–Witten invariants, ; Stationary phase integrals, quantum Toda lattices, flag manifolds, and the mirror conjecture, ; A mirror theorem for toric complete intersections, E-print hep-th/9312096E-print alg-geom/9603021E-print alg-geom/9612001E-print alg-geom/9701016 | DOI | MR | Zbl

[55] A. Marshakov, A. Mironov, A. Morozov, More evidence for the WDVV equations in $N=2$ SUSY Yang–Mills theories, E-print hep-th/9701123 | MR

[56] M. Kontsevich, Funkts. analiz i ego prilozh., 25 (1991), 50 | MR | Zbl

[57] S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, A. Zabrodin, Phys. Lett. B, 275 (1992), 311 ; ; Nucl. Phys. B, 380 (1992), 181 ; ; M. Kontsevich, Commun. Math. Phys., 147 (1992), 1 ; C. Itzykson, J.-B. Zuber, Int. J. Mod. Phys. A, 7 (1992), 5661 ; M. Adler, P. van Moerbeke, Commun. Math. Phys., 147 (1992), 25 E-print hep-th/9111037E-print hep-th/9201013 | DOI | MR | MR | DOI | MR | MR | DOI | Zbl | DOI | MR | Zbl | DOI | Zbl

[58] E. Witten, On the Kontsevich model and other models of two-dimensional gravity, Preprint IASSNS-HEP-91/24, Institute of Advanced Study, Princeton (New Jersey), USA, 1991 | MR

[59] A. Marshakov, A. Mironov, A. Morozov, Phys. Lett. B, 274 (1992), 280 | DOI | MR

[60] S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, Mod. Phys. Lett. A, 8 (1993), 1047 ; E-print hep-th/9208046 | DOI | MR | Zbl

[61] S. Kharchev, A. Marshakov, “Topological versus non-topological theories and $p$–$q$-duality in $c\nobreak1$ 2D gravity models”, String Theory, Quantum Gravity and the Unification of Fundamental Interactions, eds. M. Bianchi et al., World Scientific, Singapore, 1993, 331

[62] S. Kharchev, Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model, Preprint ITEP/TH-78/97 | MR

[63] J. Ambjørn, B. Durhuus, J. Frolich, Nucl. Phys. B, 257 [FS14] (1985), 433 | DOI | MR

[64] V. Kazakov, Mod. Phys. Lett. A, 4 (1989), 2125 ; E. Brézin, V. Kazakov, Phys. Lett. B, 236 (1990), 144 ; M. Douglas, S. Shenker, Nucl. Phys. B, 335 (1990), 635 ; D. Gross, A. Migdal, Phys. Rev. Lett., 64 (1990), 127 | DOI | MR | DOI | MR | DOI | MR | DOI | Zbl

[65] M. Fukuma, H. Kawai, R. Nakayama, Int. J. Mod. Phys. A, 6 (1991), 1385 | DOI | MR

[66] T. Eguchi, K. Hori, C. Xiong, Int. J. Mod. Phys. A, 12 (1997), 1743 ; ; Phys. Lett. B, 402 (1997), 71 ; ; T. Eguchi, M. Jinzenji, C. Xiong, Nucl. Phys. B, 510 (1998), 608 ; ; T. Eguchi, C. Xiong, Quantum cohomology at higher genus: topological recursion relations and Virasoro conditions, ; E. Getzler, Intersection theory on $\overline{\mathcal M}_{1,4}$ and elliptic Gromov–Witten invariants, ; Topological recursion relations in genus 2, ; E. Getzler, R. Pandharipande, ; E. Getzler, R. Pandharipande, Frobenius manifolds and Virasoro constraints, ; B. Dubrovin, Y. Zhang, Virasoro constraints and the Chern classes of the Hodge bundle, E-print hep-th/9605225E-print hep-th/9703086E-print hep-th/9709152E-print hep-th/9801010E-print alg-geom/9612004E-print math/9801003E-print math.ag/9805114E-print math/9805114E-print math/9808048 | DOI | MR | Zbl | MR | DOI | MR | Zbl | DOI | Zbl | MR | MR

[67] A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov, A. Orlov, Nucl. Phys. B, 357 (1991), 565 | DOI | MR

[68] S. Kharchev, A. Marshakov, A. Mironov, A. Orlov, A. Zabrodin, Nucl. Phys. B, 366 (1991), 569 | DOI | MR

[69] M. Douglas, Phys. Lett. B, 238 (1990), 176 | DOI | MR | Zbl

[70] I. Krichever, On Heisenberg relations for the ordinary linear differential operators, Preprint, ETH, Zuerich, 1990; С. П. Новиков, Функц. анализ и его прилож., 24 (1990), 43 ; G. Moore, Commun. Math. Phys., 133 (1990), 261 ; G. Moore, Matrix models of 2D gravity and isomonodromic deformations, Preprint Yale University, 1990 ; R. Schimmrigk, Phys. Rev. Lett., 65 (1990), 2483 ; P. Grinevich, S. Novikov, E-print solv-int/9501002 | MR | Zbl | DOI | MR | Zbl | MR | DOI | Zbl

[71] A. Marshakov, A. Mironov, Seiberg–Witten Systems and Whitham Hierarchies: a Short Review, Preprint FIAN/TD-04/98 ITEP/TH-51/98 | MR

[72] M. Matone, Phys. Lett. B, 357 (1995), 342 ; ; Phys. Rev. D, 53 (1996), 7354 ; ; J. Sonnenschein, S. Theisen, S. Yankielowicz, On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories, ; T. Eguchi, S. K. Yang, Mod. Phys. Lett. A, 11 (1996), 131 ; ; P. Howe, P. West, Nucl. Phys. B, 486 (1997), 425 ; E-print hep-th/9506102E-print hep-th/9506181E-print hep-th/9510129E-print hep-th/9510183E-print hep-th/9607239 | DOI | MR | MR | DOI | MR | MR | DOI | Zbl | DOI | Zbl

[73] A. Losev, N. Nekrasov, S. Shatashvili, Issues in topological gauge theoires, E-print hep-th/9711108 | MR

[74] G. Moore, E. Witten, E-print hep-th/9709193