Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes

Understand

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.