English

A Diagrammatic Equation for Oriented Planar Graphs

High Energy Physics - Theory 2015-03-13 v2 Mathematical Physics math.MP

Abstract

In this paper we introduce a diagrammatic equation for the planar sector of square non hermitian random matrix models strongly reminiscent of Polchinski's equation in quantum field theory. Our fundamental equation is first obtained by a graph counting argument and subsequently derived independently by a precise saddle point analysis of the corresponding random matrix integral. We solve the equation perturbatively for a generic model and conclude by exhibiting two duality properties of the perturbative solution.

Keywords

Cite

@article{arxiv.1003.2187,
  title  = {A Diagrammatic Equation for Oriented Planar Graphs},
  author = {Razvan Gurau},
  journal= {arXiv preprint arXiv:1003.2187},
  year   = {2015}
}

Comments

References [12] and [13] and subsequent discussion added

R2 v1 2026-06-21T14:56:20.403Z