Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

Abstract

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating functions (and the correlation functions of the lattice) obey the topological recursion, as usual in matrix models, i.e they are given by the symplectic invariants of their spectral curve.

pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor corrections

References in corpus (4)

• Conformal boundary loop models
• Boundary operators in the O(n) and RSOS matrix models
• Boundary Loop Models and 2D Quantum Gravity
• Topological expansion and boundary conditions

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• Schwinger-Dyson and loop equations for a product of square Ginibre random matrices
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