A Diagrammatic Equation for Oriented Planar Graphs

Details A Diagrammatic Equation for Oriented Planar Graphs A Diagrammatic Equation for Oriented Planar Graphs

2010-03-10

arxiv.org/abs/1003.2187v2

Nucl.Phys.B839:580-603,2010

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.nuclphysb.2010.06.022

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.

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