Hermitian matrix model free energy: Feynman graph technique for all genera
By L. Chekhov, B. Eynard. 2005
229 citations recorded by the source corpus.
We present the diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).
Subfields: Nuclear and High Energy Physics, Spectroscopy, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/50350cb5aaca217f7bc9e09eea228d11f4d2b156
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In Nuclear and High Energy Physics
In Spectroscopy
In Statistical and Nonlinear Physics
Citations in the corpus
- Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, methodology): “ge N instantons from orthogonal polynomials So far we have analyzed the \perturbative" sector of the one-cut matrix model from the point of view of the spectral curve: the procedure explained in [36, 57] gives a systematic way to compute the \perturbative" 1=N corrections in terms of data ”
- Quantum geometry of refined topological strings (2011, background): “17) and its recursion relation has been studied in [37, 38, 39].”
- Matrix eigenvalue model: Feynman graph technique for all genera (2006, methodology): “This technique, first elaborated in [16] for correlation functions in the 1MM case, was then developed for pure and mixed correlation functions in the 2MM case [21], [22] and then turned into a complete solution for the free energy first in the 1MM case [ 7 ], and then, eventually, in the 2MM case [”
- Open string amplitudes and large order behavior in topological string theory (2006, background): “We emphasize that all these results are particular cases of the recursive procedure developed in [29, 20, 32] that we just reviewed.”
- Invariants of algebraic curves and topological expansion (2007, methodology): “her cases [3,4]. The computation ofthe subleading term F(1) was done in general by Chekhov [15]. The computation to all orders of the correlation functions was found in [33], and the free energies in [17]. 10.1.1 Definition Definition 10.1 Formal 1-matrix model. Consider a ”semi-classical” potential V”
- Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings (2007, background): “This was first made clear in [37] and later culminated in the geometric formalism of [38, 39, 17].”