Loops in the Curvature Matrix Model

TL;DR

This paper studies how adding a higher order curvature term affects the properties of random surfaces in a hermitian one matrix model, revealing phase-dependent changes in surface behavior and spectrum of operators.

Contribution

It introduces a curvature perturbation to the matrix model and analyzes its impact on surface phases and operator spectra, extending understanding of matrix models in different regimes.

Findings

In the smooth phase, the model aligns with minimal conformal matter coupled to gravity.

In the intermediate phase, properties resemble discretized bosonic strings with central charge C > 1.

Perturbation alters the spectrum of scaling operators, changing surface characteristics.

Abstract

Macroscopic loop correlators are investigated in the hermitian one matrix model with the potential perturbed by the higher order curvature term. In the phase of smooth surfaces the model is equivalent to the minimal conformal matter coupled to gravity. The properties of the model in the intermediate phase are similar to that of the discretized bosonic string with the central charge $C > 1.$ Loop correlators describe the effect of the splitting of the random surfaces. It is shown, that the properties of the surfaces are changed in the intermediate phase because the perturbation modifies the spectrum of the scaling operators.