On the Nature of Nonperturbative Effects in Stabilized 2D Quantum Gravity

TL;DR

This paper investigates nonperturbative effects in stabilized 2D quantum gravity, revealing a unique vacuum structure and modifications to the loop equation through Monte Carlo simulations and theoretical analysis.

Contribution

It demonstrates the existence of a nonperturbative vacuum confined in one potential well and derives its effects on the loop equation from Ward identities.

Findings

Weak coupling regime has a unique perturbative vacuum without instantons.

Nonperturbative vacuum is confined in a single potential well.

Nonperturbative effects modify the loop equation via Ward identities.

Abstract

We remark that the weak coupling regime of the stochastic stabilization of 2D quantum gravity has a unique perturbative vacuum, which does not support instanton configurations. By means of Monte Carlo simulations we show that the nonperturbative vacuum is also confined in one potential well. Nonperturbative effects can be assessed in the loop equation. This can be derived from the Ward identities of the stabilized model and is shown to be modified by nonperturbative terms.