A Lorentzian renormalisation group equation for gauge theories
Edoardo D'Angelo, Kasia Rejzner
TL;DR
This work develops a Lorentzian functional renormalization group framework for gauge theories within the BV formalism and pAQFT on globally hyperbolic spacetimes. It introduces a local regulator $Q_k$ and an auxiliary field $\eta$, deriving a Wetterich-type flow for the effective average action $\Gamma_k$ and a Slavnov-Taylor (Zinn-Justin) master equation that constrains the functional form of $\Gamma_k$ via BRST cohomology. The authors show how to treat regulator-induced symmetry breaking through an extended BV structure, obtain an effective master equation, analyze potential anomalies, and establish compatibility of these symmetry constraints with the RG flow, including flow equations for composite operators. The framework provides a rigorous, algebraic path to study gauge theories (e.g., Yang–Mills) and gravity in Lorentzian, curved spacetimes and lays groundwork for future non-perturbative and state-dependent analyses.
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.