Integrability and Seiberg-Witten exact solution. (English) Zbl 0997.81567
Summary: The exact Seiberg-Witten (SW) description of the light sector in the \(N=2\) SUSY 4d Yang-Mills theory [N. Seiberg and E. Witten, Nucl. Phys. B 426, 19-52 (1994; Zbl 0996.81510); Nucl. Phys. B 430, No. 2, 485-486 (1994; Zbl 0996.81511)] is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevskij solution [S. P. Novikov, L. P. Pitaevskij and V. E. Zakharov Theory of solitons, English translation, Consultants Bureau, New York, (1984; Zbl 0598.35003)] to the elliptic Whitham equations. We consider this as an implication that the dynamical mechanism behind the SW solution is related to integrable systems on the moduli space of instantons. We emphasize the role of the Whitham theory as a possible substitute of the renormalization group approach to the construction of low-energy effective actions.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | Seiberg, N.; Witten, E., Nucl. Phys. B, 446, 19 (1994) |
| [2] | see also, S. Novikov, S. Manakov, L. Pitaevsky and V. Zakharov, Theory of solitons.; see also, S. Novikov, S. Manakov, L. Pitaevsky and V. Zakharov, Theory of solitons. |
| [3] | Shifman, M.; Vainshtein, A., Nucl. Phys. B, 365, 312 (1991) |
| [4] | Callan, C.; Dashen, R.; Gross, D., Phys. Rev. D, 19, 1826 (1979) |
| [5] | Levine, H.; Libby, S., Phys. Lett. B, 150, 182 (1985) |
| [6] | Gorsky, A.; Selivanov, K., Sov. Jorn. Nucl. Phys., 53, 157 (1991) |
| [7] | Dyakonov, D.; Petrov, V., Nucl. Phys. B, 245, 259 (1984) |
| [8] | Novikov, V.; Shifman, M.; Vainshtein, A.; Zakharov, V., Nucl. Phys. B, 229, 381 (1983) |
| [9] | Hitchin, N., Duke. Math. Journ., 54, N1 (1987) |
| [10] | V. Fock and A. Rosly, preprint ITEP-27/93.; V. Fock and A. Rosly, preprint ITEP-27/93. |
| [11] | Gorsky, A.; Nekrasov, N., Nucl. Phys. B, 436, 582 (1995), hepth/94021 · Zbl 1052.81607 |
| [12] | preprint CERN-TH.7538/94, LMU-TPW 94/22, hepth/941258; P. Argyres and A. Farragi, preprint IAS-94/94, hepth/9411057.; preprint CERN-TH.7538/94, LMU-TPW 94/22, hepth/941258; P. Argyres and A. Farragi, preprint IAS-94/94, hepth/9411057. |
| [13] | Krichever, I., Uspekhi Mat. Nauk, 36, N2, 12 (1981), in the Appendix to B. Dubrovin |
| [14] | Dubrovin, B.; Novikov, S., Uspekhi Mat. Nauk, 44, N6, 29 (1989) |
| [15] | Krichever, I., Funk. anal. i pril., 22, n. 3, 37-52 (1988) · Zbl 0688.35088 |
| [16] | Dijkgraaf, R.; Verlinde, E.; Verlinde, H., Nucl. Phys. B, 352, 59 (1991) |
| [17] | Krichever, I., Comm. Math. Phys., 143, 415 (1991) |
| [18] | Dubrovin, B., Comm. Math. Phys., 145, 195 (1992), preprint SISSA-89/94/FM |
| [19] | A. Losev and I. Polyubin, JETP Lett. 58 573; hepth/9305079.; A. Losev and I. Polyubin, JETP Lett. 58 573; hepth/9305079. |
| [20] | Kharchev, S.; Marshakov, A.; Mironov, A.; Morozov, A., Mod. Phys. Lett. A, 8, 1047 (1993) · Zbl 1021.81833 |
| [21] | Kharchev, S.; Marshakov, A., Int. J. Mod. Phys. A, 10, 1219 (1995) · Zbl 1044.81696 |
| [22] | C. Vafa and E. Witten, hepth/9408074.; C. Vafa and E. Witten, hepth/9408074. |
| [23] | A. Losev, G. Moore, N. Nekrasov and S. Shatashvili, to appear.; A. Losev, G. Moore, N. Nekrasov and S. Shatashvili, to appear. |
| [24] | M. Douglas and S. Shenker, preprint RU-95-12, hepth/9503163.; M. Douglas and S. Shenker, preprint RU-95-12, hepth/9503163. |
| [25] | Ya. Kogan and M. Shifman, preprint TPI-MINN-95/10-TM UMN-TH-1340-95, OUTP-95-14PM hepth/9504141.; Ya. Kogan and M. Shifman, preprint TPI-MINN-95/10-TM UMN-TH-1340-95, OUTP-95-14PM hepth/9504141. |
| [26] | A. Gorsky and A. Marshakov, preprint UUITP-7/95, to to appear; A. Gorsky and A. Marshakov, preprint UUITP-7/95, to to appear |
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