Emergent geometry from random multitrace matrix models

TL;DR

This paper proposes a new way for geometry to emerge from random multitrace matrix models, where the dimension and metric are derived from phase transition properties and eigenvalue distributions.

Contribution

It introduces a novel scenario linking phase transition critical exponents and eigenvalue laws to emergent geometry in multitrace matrix models.

Findings

Emergent geometry's dimension is determined by critical exponents.

The metric is derived from the eigenvalue distribution following Wigner's semicircle law.

No emergent geometry occurs if the uniform ordered phase is absent.

Abstract

A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent geometry is determined from the critical exponents of the disorder-to-uniform-ordered transition whereas the metric is determined from the Wigner semicircle law behavior of the eigenvalues distribution of the matrix $M$. If the uniform ordered phase is not sustained in the phase diagram then there is no emergent geometry in the multitrace matrix model.