Curvature Correlators in Nonperturbative 2D Lorentzian Quantum Gravity

TL;DR

This paper investigates a nonperturbative, diffeomorphism-invariant two-point curvature correlator in 2D Lorentzian quantum gravity using causal dynamical triangulations, finding evidence that the correlator vanishes.

Contribution

It introduces a novel nonperturbative analysis of curvature correlators in 2D Lorentzian quantum gravity with a lattice approach, addressing diffeomorphism invariance issues.

Findings

Connected two-point curvature correlator vanishes in 2D Lorentzian quantum gravity.

Uses Monte Carlo simulations to analyze correlators in a nonperturbative setting.

Provides groundwork for similar studies in higher dimensions.

Abstract

Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.