Revisiting the minimum length in the Schwinger-Keldysh formalism

TL;DR

This paper investigates the existence of a minimum length in quantum gravity using the Schwinger-Keldysh formalism and finds no evidence for a minimum geometrical length in various gravitational theories.

Contribution

It demonstrates that no minimum length arises in in-in expectation values across multiple gravitational theories, contrasting with in-out amplitude approaches.

Findings

No minimum length in in-in expectation values for quantum gravity.

Minimum length appears in in-out amplitudes related to scattering energy scales.

Non-perturbative analysis confirms absence of a minimum length in specific gravity sectors.

Abstract

The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger-Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational theories to all orders in perturbation theory. Using non-perturbative techniques, we also show that neither the conformal sector of general relativity nor higher-derivative gravity features a minimum length. A minimum length scale, on the other hand, seems to always be present when one considers in-out amplitudes, from which one could extract the energy scale of scattering processes.