Geodesic
Resolvents and Seiberg--Witten representation for a~Gaussian $\beta$-ensemble
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 96-115

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

The exact free energy of a matrix model always satisfies the Seiberg–Witten equations on a complex curve defined by singularities of the semiclassical resolvent. The role of the Seiberg–Witten differential is played by the exact one-point resolvent in this case. We show that these properties are preserved in the generalization of matrix models to $\beta$-ensembles. But because the integrability and Harer–Zagier topological recursion are still unavailable for $\beta$-ensembles, we must rely on the ordinary Alexandrov–Mironov–Morozov/Eynard–Orantin recursion to evaluate the first terms of the genus expansion. We restrict our consideration to the Gaussian model.
Keywords: matrix model, integrability, Seiberg–Witten theory.
Mots-clés : $\beta$-ensemble 
@article{TMF_2012_171_1_a8,
     author = {A. D. Mironov and A. Yu. Morozov and A. V. Popolitov and Sh. R. Shakirov},
     title = {Resolvents and {Seiberg--Witten} representation for {a~Gaussian} $\beta$-ensemble},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {96--115},
     publisher = {mathdoc},
     volume = {171},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a8/}
}
TY  - JOUR
AU  - A. D. Mironov
AU  - A. Yu. Morozov
AU  - A. V. Popolitov
AU  - Sh. R. Shakirov
TI  - Resolvents and Seiberg--Witten representation for a~Gaussian $\beta$-ensemble
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 96
EP  - 115
VL  - 171
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a8/
LA  - ru
ID  - TMF_2012_171_1_a8
ER  - 
%0 Journal Article
%A A. D. Mironov
%A A. Yu. Morozov
%A A. V. Popolitov
%A Sh. R. Shakirov
%T Resolvents and Seiberg--Witten representation for a~Gaussian $\beta$-ensemble
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 96-115
%V 171
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a8/
%G ru
%F TMF_2012_171_1_a8
A. D. Mironov; A. Yu. Morozov; A. V. Popolitov; Sh. R. Shakirov. Resolvents and Seiberg--Witten representation for a~Gaussian $\beta$-ensemble. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 96-115. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a8/