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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2013) Superpotentials, quantum parameter space and phase transitions in N=1 supersymmetric gauge theories. Journal of high energy physics (3). ISSN 10298479

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Official URL: http://dx.doi.org/10.1007/JHEP03(2013)170
URL  URL Type 

http://link.springer.com  Publisher 
http://arxiv.org/abs/1301.5982  Organisation 
Abstract
We study the superpotentials, quantum parameter space and phase transitions that arise in the study of large N dualities between N = 1 SUSY U(N) gauge theories and string models on local CalabiYau manifolds. The main tool of our analysis is a notion of spectral curve characterized by a set of complex partial ’t Hooft parameters and cuts given by projections on the spectral curve of minimal supersymmetric cycles of the underlying CalabiYau manifold. We introduce a prepotential functional via a variational problem which determines the complex density as an extremal constrained by the period conditions. This prepotential is shown to satisfy the special geometry relations of the spectral curve. We give a system of equations for the branch points of the spectral curves and determine the appropriate branch cuts as Stokes lines of a suitable set of polynomials. As an application, we use a combination of analytical and numerical methods to study the cubic model, determine the analytic condition satisfied by critical onecut spectral curves, and characterize the transition curves between the onecut and twocut phases both in the space of spectral curves and in the quantum parameter space.
Item Type:  Article 

Additional Information:  ©Springer. 
Uncontrolled Keywords:  Matrix models; Yangmills; Equations; Duality; Strings 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  34171 
Deposited On:  05 Nov 2015 18:50 
Last Modified:  10 Dec 2018 15:09 
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