Vacuum effective actions and mass-dependent renormalization in curved space

Abstract

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

arXiv comment26 pages, review prepared for the special issue of Universe collecting the contributions for the workshop "Quantum Fields - from Fundamental Concepts to Phenomenological Questions" (Mainz 26-28 September 2018), covers the results of 1803.06948 and 1812.00460

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• Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime
• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Non-minimal non-Abelian quantum vector fields in curved spacetime