Functional flows for complex effective actions

Understand

In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions.

• For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action.
• The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action.
• In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $\phi^4$-theories from zero up to four dimensions.