Proper-time flow equation and non-local truncations in quantum gravity

TL;DR

This paper investigates the flow of non-local truncations in quantum gravity, specifically analyzing the Polyakov effective action in 2D curved space, and demonstrates explicit integration of flow equations to recover the effective action.

Contribution

It introduces a method to explicitly integrate the flow of local and non-local operators in quantum gravity without relying on conformal anomaly integration.

Findings

Successfully integrated flow equations up to k=0

Recovered effective action without conformal anomaly

Provided insights into non-local truncations in quantum gravity

Abstract

We study the flow of the non-local truncation in quantum gravity and we focus in particular on the Polyakov effective action for a non-minimally coupled scalar field on a two dimensional curved space. We show that it is possible to explicitly integrate the flow of all the local and non-local operator terms up to $k=0$ and recover effective action without the integration of the conformal anomaly.