Approximate Killing symmetries in non-perturbative quantum gravity

TL;DR

This paper explores whether approximate symmetries can be identified in non-perturbative quantum gravity models, using lattice approaches and discrete calculus to analyze toy models of 2D quantum gravity.

Contribution

It introduces a method to construct and evaluate observables related to approximate Killing vectors in lattice quantum gravity models.

Findings

Feasibility of defining approximate Killing vectors in lattice quantum gravity

Construction of quantum observables using Discrete Exterior Calculus

Evaluation of observables on 2D quantum gravity toy models

Abstract

It is an open question whether fluctuations at the Planck scale in a non-perturbative theory of quantum gravity behave in such a way that the resulting semi-classical geometry can be modelled by a space that admits (approximate) Killing symmetries. We have investigated whether the notion of approximate Killing vector fields is suitable to address this question in lattice theories of quantum gravity, such as (Causal) Dynamical Triangulations. We show that it is possible to construct quantum observables related to approximate Killing vector fields using the framework of Discrete Exterior Calculus. We have evaluated the expectation value of one particular choice of observable on three toy models of two-dimensional quantum gravity.