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20
Matrix eigenvalue model: Feynman graph . . .
, 2006
"... We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint ..."
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Cited by 40 (7 self)
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We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).
Operator product expansion of higher rank Wilson loops from Dbranes and matrix models,” JHEP 0610
, 2006
"... In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N = 4 super YangMills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and Dbranes with electric ..."
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Cited by 39 (8 self)
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In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N = 4 super YangMills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and Dbranes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding
Matrix models and growth processes: From viscous flows to the quantum Hall effect,” arXiv:hepth/0412219
"... We review the recent developments in the theory of normal, normal selfdual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large N limit. The 1/N expansion of the free energy is also discussed. Our basic tool is a spe ..."
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Cited by 22 (2 self)
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We review the recent developments in the theory of normal, normal selfdual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large N limit. The 1/N expansion of the free energy is also discussed. Our basic tool is a specific Ward identity for correlation functions (the loop equation), which follows from invariance of the partition function under reparametrizations of the complex eigenvalues plane. The method for handling the loop equation requires the technique of boundary value problems in two dimensions and elements of the potential theory. As far as the physical significance of these models is concerned, we discuss, in some detail, the recently revealed applications to diffusioncontrolled growth processes (e.g., to the SaffmanTaylor problem) and to the semiclassical behaviour of electronic blobs in the quantum Hall regime. ∗Based on the lectures given at the School “Applications of Random Matrices in Physics”, Les
Formal matrix integrals and combinatorics of maps
, 2006
"... This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. ..."
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Cited by 20 (11 self)
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This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps.
Large N expansion for the 2D Dyson gas
, 2005
"... We discuss the 1/N expansion of the free energy of N logarithmically interacting charges in the plane in an external field. For some particular values of the inverse temperature β this system is equivalent to the eigenvalue version of certain random matrix models, where it is refered to as the “Dyso ..."
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Cited by 20 (1 self)
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We discuss the 1/N expansion of the free energy of N logarithmically interacting charges in the plane in an external field. For some particular values of the inverse temperature β this system is equivalent to the eigenvalue version of certain random matrix models, where it is refered to as the “Dyson gas ” of eigenvalues. To find the free energy at large N and the structure of 1/Ncorrections, we first use the effective action approach and then confirm the results by solving the loop equation. The results obtained give some new representations of the mathematical objects related to the Dirichlet boundary value problem, complex analysis and spectral geometry of exterior domains. They also suggest interesting links with bosonic field theory
Random normal matrices, Bergman kernel and projective embeddings
 JHEP 1401 (2014) 133, arXiv:1309.7333 [hepth
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CONFORMAL MAPPINGS AND DISPERSIONLESS TODA HIERARCHY II: GENERAL STRING EQUATIONS
, 2009
"... In this article, we classify the solutions of the dispersionless Toda hierarchy into degenerate and nondegenerate cases. We show that every nondegenerate solution is determined by a function H(z1, z2) of two variables. We interpret these nondegenerate solutions as defining evolutions on the space ..."
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Cited by 3 (1 self)
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In this article, we classify the solutions of the dispersionless Toda hierarchy into degenerate and nondegenerate cases. We show that every nondegenerate solution is determined by a function H(z1, z2) of two variables. We interpret these nondegenerate solutions as defining evolutions on the space D of pairs of conformal mappings (g, f), where g is a univalent function on the exterior of the unit disc, f is a univalent function on the unit disc, normalized such that g(∞) = ∞, f(0) = 0 and f ′ (0)g ′ (∞) = 1. For each solution, we show how to define the natural time variables tn, n ∈ Z, as complex coordinates on the space D. We also find explicit formulas for the tau function of the dispersionless Toda hierarchy in terms of H(z1, z2). Imposing some conditions on the function H(z1, z2), we show that the dispersionless Toda flows can be naturally restricted to the subspace Σ of D defined by f(w) = 1/g(1 / ¯w). This recovers the result of Zabrodin [28].
Fermions in the harmonic potential and string theory
, 2004
"... We explicitly derive collective field theory description for the system of fermions in the harmonic potential. This field theory appears to be a coupled system of free scalar and (modified) Liouville field. This theory should be considered as an exact bosonization of the system of nonrelativistic f ..."
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Cited by 2 (0 self)
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We explicitly derive collective field theory description for the system of fermions in the harmonic potential. This field theory appears to be a coupled system of free scalar and (modified) Liouville field. This theory should be considered as an exact bosonization of the system of nonrelativistic fermions in the harmonic potential. Being surprisingly similar to the worldsheet formulation of c = 1 string theory, this theory has quite different physical features and it is conjectured to give spacetime description of the string theory, dual to the fermions in the harmonic potential. A vertex operator in this theory is shown to be a field theoretical representation of the local fermion operator, thus describing a D0 brane in the string language. Possible generalization of this result and its derivation for the case of c = 1 string theory (fermions in the inverse harmonic potential) is discussed. 1 Introduction and