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Journal Article

Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes


Bautista,  Teresa
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Bautista, T., Benevides, A., & Dabholkar, A. (2018). Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes. Journal of high energy physics: JHEP, 2018(06): 055. doi:10.1007/JHEP0(2018)055.

Cite as: http://hdl.handle.net/11858/00-001M-0000-002E-250A-B
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.