An algebraic QFT approach to the Wetterich equation on Lorentzian manifolds

TL;DR

This paper develops a covariant flow equation for scalar quantum field theories on Lorentzian manifolds using algebraic QFT techniques, revealing fixed points in thermal and de Sitter states.

Contribution

It introduces a local regulator-based flow equation for QFT on Lorentzian manifolds, extending the Wetterich equation to curved spacetimes with a covariant approach.

Findings

Fixed points found in thermal states.

Fixed points identified in Bunch-Davies vacuum on de Sitter.

Method applicable to generic Lorentzian backgrounds.

Abstract

We discuss the scaling of the effective action for the interacting scalar quantum field theory on generic spacetimes with Lorentzian signature and in a generic state (including vacuum and thermal states, if they exist). This is done constructing a flow equation, which is very close to the renown Wetterich equation, by means of techniques recently developed in the realm of perturbative Algebraic Quantum Field theory (pAQFT). The key ingredient that allows one to obtain an equation which is meaningful on generic Lorentzian backgrounds is the use of a local regulator, which keeps the theory covariant. As a proof of concept, the developed methods are used to show that non-trivial fixed points arise in quantum field theories in a thermal state and in the case of quantum fields in the Bunch-Davies state on the de Sitter spacetime.