Asymptotic Quantum Gravity as an Infrared Geometric Theory

TL;DR

This paper develops an effective geometric framework for the infrared sector of asymptotically flat quantum gravity, revealing how asymptotic states and superselection sectors are organized through a Berry connection induced by integrating out bulk modes.

Contribution

It introduces a novel geometric description of infrared quantum gravity using a Born-Oppenheimer reduction and Berry connection, emphasizing global consistency over spectral analysis.

Findings

Infrared gravitational states form superselection sectors labeled by holonomy.

The reduced density matrix includes a geometric contribution from the Berry connection.

Quantization emerges from adiabatic transport conditions, not spectral properties.

Abstract

We formulate the infrared sector of asymptotically flat quantum gravity in terms of asymptotic configurations accessible to external observers. Starting from the Regge-Teitelboim Hamiltonian that generates physical evolution in the presence of gravitational constraints, we perform a Born-Oppenheimer reduction separating slow asymptotic data from fast bulk gravitational fluctuations. We show that integrating out the fast sector induces a functional Berry connection over the space of asymptotic charges, so that the effective infrared dynamics is governed by parallel transport on this charge space. In this framework, infrared gravitational states are naturally organized into superselection sectors labelled by the holonomy of the induced connection, and the reduced density matrix obtained after tracing over ultraviolet bulk modes acquires a geometric contribution. This provides an effective geometric description of the asymptotic quantum gravitational sector, where quantization arises as a global consistency condition under adiabatic transport rather than as a spectral property of local bulk operators.