Collective Field Theory for D=0 Matrix Models

TL;DR

This paper explores the non-perturbative features of zero-dimensional matrix models, highlighting large-N subtleties and linking eigenvalue tunneling to chaotic recursion sequences in orthogonal polynomial analysis.

Contribution

It introduces a novel perspective on eigenvalue tunneling in matrix models through the lens of chaotic recursion coefficients, advancing understanding of non-perturbative effects.

Findings

Eigenvalue tunneling corresponds to chaotic recursion sequences.

Large-N limit subtleties affect semiclassical analysis.

Orthogonal polynomial recursion coefficients encode tunneling phenomena.

Abstract

I investigate non-perturbative aspects of zero-dimensional matrix models. Subtleties in the large-$N$ limit of the semiclassical picture are pointed out. The tunneling of eigenvalues is seen to correspond to a chaotic sequence of recursion coefficients determining the orthogonal polynomials.