Instantons in the Quantum Framework of 2D Gravity

TL;DR

This paper investigates non-perturbative phenomena in 2D quantum gravity through stochastic regularization of matrix models, revealing instanton-like behavior and connecting semiclassical approximations to quantum eigenvalue densities.

Contribution

It demonstrates the correspondence between WKB approximation and eigenvalue density, and explores the universal instanton-like features in the double scaled potential.

Findings

WKB approximation matches the semiclassical eigenvalue density.

The double scaled potential shows universal instanton-like behavior.

Interpretation of instantons in pure gravity remains open.

Abstract

We analyze the non--perturbative features of 2D quantum gravity defined by stochastic regularization of the unstable matrix model showing, first, that the WKB approximation of the well-defined quantum Fokker-Planck hamiltonian corresponds to the semiclassical eigenvalue density of the former. The double scaled potential exhibits an instanton--like behaviour, which is universal and scales, but whose interpretation in terms of pure gravity is still open.