Stochastic Quantization vs. KdV Flows in 2D Quantum Gravity

TL;DR

This paper investigates stochastic quantization in 2D quantum gravity, showing it does not follow KdV flow equations and differs from matrix models, with analysis of key physical quantities.

Contribution

It demonstrates that stochastic quantization does not satisfy KdV flow equations, contrasting with matrix models, and analyzes related physical behaviors.

Findings

Stochastic quantization does not satisfy KdV flow equations.

It differs from matrix models that do allow real solutions.

Behavior of Fermi energy, free energy, and macroscopic loops is elucidated.

Abstract

We consider the stochastic quantization scheme for a non-perturbative stabilization of 2D quantum gravity and prove that it does not satisfy the KdV flow equations. It therefore differs from a recently suggested matrix model which allows real solutions to the KdV equations. The behaviour of the Fermi energy, the free energy and macroscopic loops in the stochastic quantization scheme are elucidated.