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 the anomalous leading large logarithms of the scale factor, log a(x), 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 R2 ≪ ∇2R 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 R2 ≫ ∇2R, which is often of interest in cosmology.
Highlights
To obtain the full nonlocal effective action, one could use the covariant nonlocal expansion of the heat kernel developed by Barvinsky, Vilkovisky, and collaborators [3, 4]
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
Summary
We describe the general method for computing the quantum effective action at the one-loop order for essentially all the standard model fields in Weyl-flat spacetimes by integrating the Weyl anomaly. We ignore Yukawa couplings and work in the conformal massless limit so that all couplings are dimensionless. Classical Weyl invariance is not fundamentally necessary to integrate the Weyl anomaly in order to compute the effective action. It does simplify the computation of the anomaly. We first review elements of the background field method and gauge fixing to. We discuss the anomalies in terms of the Schwinger-DeWitt expansion and a lemma to obtain the effective action by integrating the anomaly
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