Enumeration of N-rooted maps using quantum field theory

Abstract

A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e-N+1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N-rooted maps and for the numbers of N-rooted maps with a given number of edges using the path integral approach applied to the corresponding quantum field theory.

27 pages, 7 figures

References in corpus (1)

• A bijection for rooted maps on general surfaces

Cited by in corpus (2)

• Double-logarithms in N=8 supergravity: impact parameter description and mapping to 1-rooted ribbon graphs
• Feynman diagrams, ribbon graphs, and topological recursion of Eynard-Orantin