Quantum gravitational corrections to the propagator in spacetimes with constant curvature

TL;DR

This paper investigates how quantum gravitational effects, incorporating a fundamental length scale, modify scalar field propagators in constant curvature spacetimes, resulting in ultraviolet finite and non-perturbative corrections.

Contribution

It introduces a method to compute quantum gravitational modifications to propagators that are UV finite and non-perturbative, using the path integral duality hypothesis.

Findings

Modified propagators are ultraviolet finite.

Corrections are non-perturbative in the Planck length.

Results have implications for quantum gravity models.

Abstract

The existence of a minimal and fundamental length scale, say, the Planck length, is a characteristic feature of almost all the models of quantum gravity. The presence of the fundamental length is expected to lead to an improved ultra-violet behavior of the semi-classical propagators. The hypothesis of path integral duality provides a prescription to evaluate the modified propagator of a free, quantum scalar field in a given spacetime, taking into account the existence of the fundamental length in a locally Lorentz invariant manner. We use this prescription to compute the quantum gravitational modifications to the propagators in spacetimes with constant curvature, and show that: (i) the modified propagators are ultra-violet finite, and (ii) the modifications are non-perturbative in the Planck length. We discuss the implications of our results.