Functional flows for complex effective actions

TL;DR

This paper develops a functional renormalisation group framework for computing complex effective actions, enabling analysis of phase transitions and Lee-Yang zeros in quantum field theories.

Contribution

It introduces a general approach for complex effective actions, comparing Wilsonian and 1PI flows, and extends to complex fields in b4b4-theories and potential QCD applications.

Findings

Validated the Legendre transform for complex actions against exact zero-dimensional results.

Obtained effective potentials for complex b4b4-theories in up to four dimensions.

Determined Lee-Yang zeros for various parameter values.

Abstract

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. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.