Wilsonian flows and background fields

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.