Non-perturbative 2d quantum gravity and hamiltonians unbounded from below

TL;DR

This paper demonstrates how stochastic stabilization enables weak and strong coupling expansions in 2d quantum gravity, with a focus on a Hamiltonian that is unbounded below but has a discrete spectrum.

Contribution

It introduces a stochastic stabilization approach that yields both weak and strong coupling expansions in 2d quantum gravity with a novel Hamiltonian.

Findings

Stochastic stabilization provides the genus expansion.

The double scaling limit involves an unbounded Hamiltonian.

The Hamiltonian has a discrete spectrum despite being unbounded.

Abstract

We show how the stochastic stabilization provides both the weak coupling genus expansion and a strong coupling expansion of 2d quantum gravity. The double scaling limit is described by a hamiltonian which is unbounded from below, but which has a discrete spectrum.