Nonperturbative Ground State of the Stochastic Stabilization of 2D Quantum Gravity

TL;DR

This paper constructs the nonperturbative ground state of a stabilized 2D quantum gravity model derived from matrix models, revealing similarities in nonperturbative behavior and modifications to loop equations.

Contribution

It provides the first nonperturbative construction of the ground state for the stochastic stabilization of 2D quantum gravity matrix models.

Findings

Nonperturbative ground state combines perturbative and nonperturbative wave functions.

Nonperturbative effects modify the loop equation.

Similar nonperturbative behavior from stabilized model and string equation.

Abstract

I construct the ground state, up to first nonperturbative order, of the stochastic stabilization of the zero dimensional matrix model which defines 2D Quantum Gravity. It is given by the linear combination of a perturbative wave function and a nonperturbative one. The nonperturbative behaviour which arise from the stabilized model and from the string equation are similar. I show the modification of the loop equation by nonperturbative contribution.