A Diagrammatic Equation for Oriented Planar Graphs

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.

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

References in corpus (6)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Group field theory renormalization - the 3d case: power counting of divergences
• Topological Graph Polynomials in Colored Group Field Theory
• Scaling behaviour of three-dimensional group field theory
• Linearized Group Field Theory and Power Counting Theorems
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field

Cited by in corpus (3)

• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions