Free energy topological expansion for the 2-matrix model
By L. Chekhov, B. Eynard, N. Orantin. 2006
190 citations recorded by the source corpus.
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4b61a0ada4d20de5be3568507ff429bec3338af1
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In Geometry and Topology
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Matrix eigenvalue model: Feynman graph technique for all genera (2006, methodology): “…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).”
- Open string amplitudes and large order behavior in topological string theory (2006, background): “, zh) defined by the recursive procedure of [29, 21, 32] (the holomorphic anomaly equation for the annulus amplitude is written down in (2.”
- Invariants of algebraic curves and topological expansion (2007, methodology): “Keeping on following [ 19 ], one finds that the topological expansion of the free energy also coincides with the special free energies defined on 4-16, that is the τ-function of the algebraic curve.”