A Generating Function for Fatgraphs

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.

24 pages, uses harvmac macro, 1 figure not included, Saclay preprint SPhT/92-162

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