A Lorentzian renormalisation group equation for gauge theories

TL;DR

This paper develops a Lorentzian renormalisation group flow equation for gauge theories using the BV formalism, ensuring gauge invariance and consistency within a cohomological framework.

Contribution

It introduces a Wetterich-type flow equation for gauge theories on Lorentzian manifolds, extending previous scalar field work and incorporating Slavnov-Taylor identities.

Findings

Derived a Lorentzian flow equation for gauge theories.

Showed the effective action satisfies Slavnov-Taylor identities.

Demonstrated the flow's consistency with gauge invariance.

Abstract

In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation governs the flow of the effective average action, under changes of a mass parameter k. Here we introduce an analogous flow equation for gauge theories, with the aid of the Batalin-Vilkovisky (BV) formalism. We also show that the corresponding effective average action satisfies a Slavnov-Taylor identity in Zinn-Justin form. We interpret the equation as a cohomological constraint on the functional form of the effective average action, and we show that it is consistent with the flow.