Towards reconstructing the quantum effective action of gravity

TL;DR

This paper develops a formalism to reconstruct the quantum effective action of gravity from correlation functions, applying it to Causal Dynamical Triangulations data to identify Einstein-Hilbert and non-local terms.

Contribution

It introduces a new matching-template formalism to infer effective gravitational actions from observable correlation functions, bridging fundamental theory and low-energy physics.

Findings

Effective action includes Einstein-Hilbert and non-local terms

Correlation functions can be used to reverse-engineer gravitational couplings

Formalism applicable to various quantum gravity approaches

Abstract

Starting from a parameterisation of the quantum effective action for gravity we calculate correlation functions for observable quantities. The resulting templates allow to reverse-engineer the couplings describing the effective dynamics from the correlation functions. Applying this new formalism to the autocorrelation function of spatial volume fluctuations measured within the Causal Dynamical Triangulations program suggests that the corresponding quantum effective action consists of the Einstein-Hilbert action supplemented by a non-local interaction term. We expect that our matching-template formalism can be adapted to a wide range of quantum gravity programs allowing to bridge the gap between the fundamental formulation and observable low-energy physics.