Wilsonian flows and background fields

TL;DR

This paper investigates the use of background field dependent regularisations in exact renormalisation group flows, clarifies the role of implicit scale dependence, and evaluates its impact numerically for scalar theories, with implications for gauge theories.

Contribution

It demonstrates that proper-time flows approximate exact background field flows for certain regulators and analyzes the effects of implicit scale dependence in these flows.

Findings

Proper-time flows approximate exact background field flows for specific regulators.

Numerical evaluation shows the impact of implicit scale dependence varies with approximations.

Implications for gauge theories are discussed, indicating broader relevance.

Abstract

We study exact renormalisation group flows for background field dependent regularisations. It is shown that proper-time flows are approximations to exact background field flows for a specific class of regulators. We clarify the role of the implicit scale dependence introduced by the background field. Its impact on the flow is evaluated numerically for scalar theories at criticality for different approximations and regularisations. Implications for gauge theories are discussed.