Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes

TL;DR

This paper presents an efficient method to compute nonlocal quantum effective actions for Weyl-flat spacetimes, enabling analysis of quantum effects in cosmology and holography with improved validity over existing approaches.

Contribution

It introduces a novel approach using the Weyl anomaly and local renormalization group equations to re-sum leading logarithms, extending the applicability of covariant perturbation theory.

Findings

Derived quantum effective actions for Yang-Mills and scalar fields.

Method re-sums covariant perturbation theory to all orders in curvature.

Applicable in regimes with large curvature variations, relevant for cosmology.

Abstract

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite $N$ corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of leading large logarithms in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime $R^{2} \ll \nabla^{2} R $ for a typical curvature scale $R$, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime $R^{2} \gg \nabla^{2} R$, which is often of interest in cosmology.