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.
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