Topological expansion for the 1-hermitian matrix model correlation functions
نویسنده
چکیده
We rewrite the loop equations of the hermitian matrix model, in a way which involves no derivative with respect to the potential, we compute all the correlation functions, to all orders in the topological 1/N expansion, as residues on an hyperelliptical curve. Those residues, can be represented as Feynmann graphs of a cubic field theory on the curve.
منابع مشابه
Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
We rewrite the loop equations of the hermitian 2-matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological 1/N expansion, as residues on an algebraic curve. Those residues, can be represented diagrammatically as Feynman graphs of a cubic interaction field theory on the curve.
متن کاملGeneralized Penner models to all genera.
We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to investigate the scaling behaviour of the model in the vicinity of these points. We carry out an analysis of the critical behaviour to all genera addressing all types ...
متن کاملThe Matrix Model for Dessins D’enfants
We present the matrix models that are the generating functions for branched covers of the complex projective line ramified over 0, 1, and∞ (Grotendieck’s dessins d’enfants) of fixed genus, degree, and the ramification profile at infinity. For general ramifications at other points, the model is the two-logarithm matrix model with the external field studied previously by one of the authors (L.Ch....
متن کاملLarge N expansion of the 2 - matrix model
We present a method, based on loop equations, to compute recursively, all the terms in the large N topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.
متن کاملNonperturbative effects and nonperturbative definitions in matrix models and topological strings
We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide...
متن کامل