Edoardo D’Angelo: Wetterich equation on lorentzian manifolds

The Wetterich equation governs the renormalization flow of the effective action under the scaling of an IR cutoff. In this talk, I introduce a generalization of the Wetterich approach to scalar field theories in generic, Hadamard states on globally hyperbolic, Lorentzian spacetimes, using techniques developed in the perturbative Algebraic Quantum Field Theory framework. The main novel ingredient is the use of a local regulator, which preserves the local covariance and unitarity of the theory while regularizing the infrared divergences. As a proof of concept, I also briefly discuss the application of the theory to thermal states in Minkowski and to the Bunch-Davies vacuum in de Sitter space.