Nonlocal quantum effective actions in WeylFlat spacetimes
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 Weylflat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local SchwingerDeWitt expansion of the heat kernel and allows for a resummation of the anomalous leading large logarithms of the scale factor, log a( x), in situations where the Weyl factor changes by several efoldings. As an illustration, we obtain the quantum effective action for the YangMills field coupled to massless matter, and the selfinteracting massless scalar field. Our action reduces to the nonlocal action obtained using the BarvinskyVilkovisky covariant perturbation theory in the regime R ^{2} ≪ ∇^{2} R for a typical curvature scale R, but has a greater range of validity effectively resumming the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R ^{2} ≫ ∇^{2} R, which is often of interest in cosmology.
 Publication:

Journal of High Energy Physics
 Pub Date:
 June 2018
 DOI:
 10.1007/JHEP06(2018)055
 arXiv:
 arXiv:1711.00135
 Bibcode:
 2018JHEP...06..055B
 Keywords:

 Anomalies in Field and String Theories;
 Effective Field Theories;
 Renormalization Group;
 Models of Quantum Gravity;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 24 pages