English

Topological expansion and boundary conditions

High Energy Physics - Theory 2009-11-13 v2 Mathematical Physics math.MP

Abstract

In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.

Keywords

Cite

@article{arxiv.0710.0223,
  title  = {Topological expansion and boundary conditions},
  author = {Bertrand Eynard and Nicolas Orantin},
  journal= {arXiv preprint arXiv:0710.0223},
  year   = {2009}
}

Comments

latex, 25 pages. few misprints corrected

R2 v1 2026-06-21T09:24:24.931Z