Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants

TL;DR

This paper computes mixed correlation functions in a two-matrix model to count bicolored surfaces and proves an x-y symmetry property of associated algebraic invariants, advancing understanding of matrix models and their geometric interpretations.

Contribution

It introduces a method to compute mixed traces in the two-matrix model and establishes the x-y symmetry of the algebraic curve invariants, linking combinatorics and algebraic geometry.

Findings

Computed expectation values of mixed traces in the two-matrix model.

Proved x-y symmetry of algebraic curve invariants.

Connected matrix model correlations with geometric surface counting.

Abstract

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform boundary conditions. As an application, we prove the $x-y$ symmetry of the algebraic curve invariants introduced in math-ph/0702045.