Matrix Model Perturbed by Higher Order Curvature Terms

TL;DR

This paper investigates a zero-dimensional matrix model with higher order curvature perturbations, revealing phase structures similar to discretized string theories, including smooth surfaces, intermediate phases, and branched polymers.

Contribution

It introduces a matrix model perturbed by nonlocal higher order curvature terms and analyzes its phase diagram, connecting it to discretized string theories.

Findings

The phase diagram includes smooth, intermediate, and branched polymer phases.

Perturbations are irrelevant in the smooth phase and dominant in the branched polymer phase.

The model exhibits features analogous to discretized Polyakov's bosonic string with higher curvature.

Abstract

The critical behaviour of the $D=0$ matrix model with potential perturbed by nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of discretized Polyakov's bosonic string with higher order curvature terms included. It contains the phase of smooth (Liouville) surfaces, the intermediate phase and the phase of branched polymers. The perturbation becomes irrelevant at the first phase and dominates at the third one.