On powercounting in perturbative quantum gravity theories through color-kinematic duality

TL;DR

This paper explores how color-kinematic duality can be used to improve powercounting estimates of UV divergences in quantum gravity, potentially explaining cancellations beyond traditional methods.

Contribution

It introduces a systematic approach to powercounting in gravity theories using color-kinematic duality and reformulates the duality with linear maps, addressing loop-level subtleties.

Findings

BCFW shifts of gravity integrands are loop-order independent under duality assumptions

Cancellations in UV divergence estimates depend on duality implementation and graph topology

Evidence suggests duality may hold at all loop orders in gauge theories

Abstract

The standard argument why gravity is not renormalisable relies on direct powercounting of Feynman graphs to estimate the degree of UV divergence. This analysis has in several (highly) supersymmetric examples be shown to overestimate divergences considerably. In these examples the main improvements arise from a conjectured duality between color and kinematics. In this paper we initiate the systematic study of quite general powercounting under the assumption that color-kinematic duality exists. The main technical tool is a reformulation of the duality in terms of linear maps, modulo subtleties at loop level mostly inherent to the duality. This tool may have wider applications in both gauge and gravity theories, up to resolution of the subtleties. Here it is first applied to the large Britto-Cachazo-Feng-Witten (BCFW) shift behavior of gravity integrands constructed through the duality. Assuming color-kinematic duality and reasonable technical requirements hold these shifts are shown to be independent of loop order, which would imply massive cancellations with respect to the Feynman graph expression. More speculatively, the same approach is then applied to provide estimates of the overall degree of UV divergence in quite general gravity theories, assuming the duality exists. The cancellations obtained in these estimates depends on the exact implementation of the duality at loop level, especially on graph topology. Finally, some evidence for the duality to all loop orders is provided from an analysis of BCFW shifts of gauge theory integrands through Feynman graphs.