Geodesic
On the microscopic origin of integrability in the Seiberg–Witten
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 424-450 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss the microscopic origin of integrability in the Seiberg–Witten theory. In particular, we discuss the theory in more detail with the simplest higher perturbation in the ultraviolet, where additional explicit results are obtained using bosonization and elliptic uniformization of the spectral curve.
Keywords: gauge theory, integrable system, instanton, Riemann surface. 
@article{TMF_2008_154_3_a2,
     author = {A. V. Marshakov},
     title = {On the microscopic origin of integrability in the {Seiberg{\textendash}Witten}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {424--450},
     year = {2008},
     volume = {154},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a2/}
}
TY  - JOUR
AU  - A. V. Marshakov
TI  - On the microscopic origin of integrability in the Seiberg–Witten
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 424
EP  - 450
VL  - 154
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a2/
LA  - ru
ID  - TMF_2008_154_3_a2
ER  - 
%0 Journal Article
%A A. V. Marshakov
%T On the microscopic origin of integrability in the Seiberg–Witten
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 424-450
%V 154
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a2/
%G ru
%F TMF_2008_154_3_a2
A. V. Marshakov. On the microscopic origin of integrability in the Seiberg–Witten. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 424-450. http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a2/

[1] A. Marshakov, N. Nekrasov, JHEP, 2007, no. 1, 104 ; arXiv: hep-th/0612019 | DOI | MR

[2] I. M. Krichever, Comm. Pure Appl. Math., 47:4 (1994), 437–475 ; arXiv: hep-th/9205110 | DOI | MR | Zbl

[3] N. Seiberg, E. Witten, Nucl. Phys. B, 426:1 (1994), 19–52 ; Erratum, 430 (1994), 485–486 ; arXiv: hep-th/9407087 | DOI | MR | Zbl | DOI | MR | Zbl

[4] A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, A. Morozov, Phys. Lett. B, 355:3–4 (1995), 466–474 ; arXiv: hep-th/9505035 | DOI | MR | Zbl

[5] N. A. Nekrasov, Adv. Theor. Math. Phys., 7:5 (2003), 831–864 ; arXiv: hep-th/0206161 | DOI | MR | Zbl

[6] A. S. Losev, A. Marshakov, N. Nekrasov, “Small instantons, little strings and free fermions”, From Fields to Strings: Circumnavigating Theoretical Physics, Ian Kogan Memorial Volume, eds. M. Shifman, A. Vainshtein, J. Wheater, World Scientific, Singapore, 2005, 581–621 ; arXiv: hep-th/0302191 | DOI | MR | Zbl

[7] A. Okounkov, R. Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, arXiv: math.AG/0204305

[8] K. Ueno, K. Takasaki, Adv. Stud. Pure Math., 4 (1984), 1–95 | MR | Zbl

[9] M. Jimbo, T. Miwa, Publ. RIMS Kyoto Univ., 19:3 (1983), 943–1001 | DOI | MR | Zbl

[10] G. I. Olshanskii, Vvedenie v algebraicheskuyu kombinatoriku, http://www.mccme.ru/ ium/s04/algcomb.html

[11] N. Nekrasov, A. Okounkov, “Seiberg–Witten theory and random partitions”, The Unity of Mathematics, Progr. Math., 244, Birkhäuser, Boston, MA, 2006, 525–596 ; arXiv: hep-th/0306238 | DOI | MR | Zbl

[12] M. Toda, Teoriya nelineinykh reshetok, Mir, M., 1984 | MR | MR | Zbl

[13] M. Kontsevich, Comm. Math. Phys., 147:1 (1992), 1–23 ; S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, A. Zabrodin, Nucl. Phys. B, 380:1–2 (1992), 181–240 ; arXiv: hep-th/9201013 | DOI | MR | Zbl | DOI | MR

[14] A. Orlov, Hypergeometric tau functions $\tau({\mathbf t},T,{\mathbf t}^*)$ as $\infty$-soliton tau function in $T$ variables, ; E. Bettelheim, A. Abanov, P. Wiegmann, J. Phys. A, 40:8 (2007), F193–F207 ; arXiv: nlin/0305001arXiv: nlin.SI/0605006 | DOI | MR | Zbl

[15] N. Nekrasov, Nucl. Phys. B, 531:1–3 (1998), 323–344 ; ; A. E. Lawrence, N. Nekrasov, Nucl. Phys. B, 513:1–2 (1998), 239–265 ; ; H. W. Braden, A. Marshakov, A. Mironov, A. Morozov, Phys. Lett. B, 448:3–4 (1999), 195–202 ; ; Nucl. Phys. B, 558:1–2 (1999), 371–390 ; arXiv: hep-th/9609219arXiv: hep-th/9706025arXiv: hep-th/9812078arXiv: hep-th/9902205 | DOI | MR | Zbl | MR | DOI | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[16] T. Maeda, T. Nakatsu, K. Takasaki, T. Tamakoshi, Nucl. Phys. B, 715:1–2 (2005), 275–303 ; arXiv: hep-th/0412329 | DOI | MR | Zbl

[17] A. V. Marshakov, TMF, 147:2 (2006), 163–228 ; arXiv: hep-th/0601212 | DOI | MR | Zbl

[18] I. Kostov, I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin, “The $\tau$-function for analytic curves”, Random Matrix Models and Their Applications, Math. Sci. Res. Inst. Publ., 40, Cambridge Univ. Press, Cambridge, 2001, 285–299 ; ; A. Marshakov, P. Wiegmann, A. Zabrodin, Comm. Math. Phys., 227:1 (2002), 131–153 ; ; I. Krichever, A. Marshakov, A. Zabrodin, Comm. Math. Phys., 259:1 (2005), 1–44 ; arXiv: hep-th/0005259arXiv: hep-th/0109048arXiv: hep-th/0309010 | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[19] A. S. Losev, N. Nekrasov, S. Shatashvili, Nucl. Phys. B, 534:3 (1998), 549–611 ; arXiv: hep-th/9711108 | DOI | MR | Zbl

[20] B. F. Logan, L. A. Shepp, Adv. Math., 26:2 (1977), 206–222 ; С. В. Керов, А. М. Вершик, ДАН СССР, 233:6 (1977), 1024–1027 ; С. В. Керов, Теория вероятн. и ее примен., 31:3 (1986), 627–628; А. М. Вершик, Зап. науч. сем. ЛОМИ, 172 (1989), 3–20 | DOI | MR | Zbl | MR | Zbl | MR | Zbl

[21] J. D. Fay, Theta-Functions on Riemann Surfaces, Lecture Notes in Math., 352, Springer, Berlin–New York, 1973 | DOI | MR | Zbl

[22] A. Gorsky, A. Marshakov, A. Mironov, A. Morozov, Nucl. Phys. B, 527:3 (1998), 690–716 ; arXiv: hep-th/9802007 | DOI | MR | Zbl