Geodesic
Free energy of the two-dimensional $U(n)$-gauge field theory on the sphere
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 3, pp. 389-401 
B. A. de Monvel; M. V. Shcherbina. Free energy of the two-dimensional $U(n)$-gauge field theory on the sphere. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 3, pp. 389-401. http://geodesic.mathdoc.fr/item/TMF_1998_115_3_a4/
@article{TMF_1998_115_3_a4,
     author = {B. A. de Monvel and M. V. Shcherbina},
     title = {Free energy of the two-dimensional $U(n)$-gauge field theory on the sphere},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {389--401},
     year = {1998},
     volume = {115},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_115_3_a4/}
}
TY  - JOUR
AU  - B. A. de Monvel
AU  - M. V. Shcherbina
TI  - Free energy of the two-dimensional $U(n)$-gauge field theory on the sphere
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 389
EP  - 401
VL  - 115
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_115_3_a4/
LA  - ru
ID  - TMF_1998_115_3_a4
ER  - 
%0 Journal Article
%A B. A. de Monvel
%A M. V. Shcherbina
%T Free energy of the two-dimensional $U(n)$-gauge field theory on the sphere
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 389-401
%V 115
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1998_115_3_a4/
%G ru
%F TMF_1998_115_3_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

The partition function of the two-dimensional $U(n)$-gauge field theory in the limit $n\to\infty$ is rigorously derived. Recent studies in the theory of random matrices combined with the traditional tools of statistical mechanics were the stimuli for the methods used and the results obtained.

[1] M. Duglas, V. Kazakov, Phys. Lett. B, 319 (1993), 219 | DOI

[2] J.-M. Daul, V. Kazakov, Wilson Loop for Large $N$ Yang-Mills Theory on a Two Dimensional Sphere, Preprint LPTENS N93/37, 1993 | MR

[3] V. Kazakov, T. Wynter, Nucl. Phys. B, 440 (1995), 407 | DOI | MR | Zbl

[4] M. L. Mehta, Random Matrices, Academic Press, New York, 1991 | MR | Zbl

[5] E. Brezin, C. Itzykson, G. Parisi, J. Zuber, Commun. Math. Phys., 59 (1978), 35 | DOI | MR | Zbl

[6] D. Bessis, C. Itzykson, J. Zuber, Adv. Appl. Math., 1 (1980), 109 | DOI | MR | Zbl

[7] A. B. de Monvel, L. Pastur, M. Shcherbina, J. Stat. Phys., 79 (1995), 585 | DOI | MR | Zbl

[8] N. I. Muskhelishvili, Singular Integral Equations, P. Noordhoff, Groningen, 1953 | MR

[9] M. V. Scherbina, TMF, 81 (1989), 134 | MR

[10] N. N. Bogolyubov, ml., Metod approksimiruyuschego gamiltoniana, Nauka, M., 1971