Every Feynman diagram in a two-matrix model is mapped to a unique closed string worldsheet and Belyi embedding, with the diagram's weight equal to the string action.
A Generating Function for Fatgraphs
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abstract
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi--classical computations, leading in particular to a closed formula corresponding to (genus zero, connected) trees.
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Strings from Feynman Diagrams
Every Feynman diagram in a two-matrix model is mapped to a unique closed string worldsheet and Belyi embedding, with the diagram's weight equal to the string action.