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Konopelchenko, Boris and Martínez Alonso, Luis and Medina, Elena (2013) Spectral curves in gauge/string dualities: integrability, singular sectors and regularization. Journal of physics A: Mathematical and theoretical, 46 (22). ISSN 17518113

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Official URL: http://dx.doi.org/10.1088/17518113/46/22/225203
URL  URL Type 

http://iopscience.iop.org  Publisher 
http://arxiv.org/abs/1301.7082  Organisation 
Abstract
We study the moduli space of the spectral curves y ^2 = W ‘ (z) ^2 + f(z) which characterize the vacua of N = 1 U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential W(z). The integrable structure of the Whitham equations is used to determine the spectral curves from their moduli. An alternative characterization of the spectral curves in terms of critical points of a family of polynomial solutions W to EulerPoissonDarboux equations is provided. The equations for these critical points are a generalization of the planar limit equations for onecut random matrix models. Moreover, singular spectral curves with higher order branch points turn out to be described by degenerate critical points of W. As a consequence we propose a multiple scaling limit method of regularization and show that, in the simplest cases, it leads to the PainlevèI equation and its multicomponent generalizations.
Item Type:  Article 

Additional Information:  ©IOP Publishing Ltd. 
Uncontrolled Keywords:  Matrix models; Orthogonal polynomials; Asymptotics 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  33894 
Deposited On:  04 Nov 2015 17:57 
Last Modified:  10 Dec 2018 15:09 
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