Nonlocal quantum effective actions in Weyl-Flat spacetimes

  • Teresa Bautista
  • André Benevides
  • Atish Dabholkar
Open Access
Regular Article - Theoretical Physics


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.


Anomalies in Field and String Theories Effective Field Theories Renormalization Group Models of Quantum Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Teresa Bautista
    • 1
  • André Benevides
    • 2
    • 3
  • Atish Dabholkar
    • 3
    • 4
    • 5
  1. 1.Max Planck Institute for Gravitational Physics (Albert Einstein Institute)PotsdamGermany
  2. 2.Scuola Internazionale Superiore di Studi Avanzati (SISSA)TriesteItaly
  3. 3.Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  4. 4.Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHEParisFrance
  5. 5.CNRS, UMR 7589, LPTHEParisFrance

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