Functional flows for complex effective actions

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^4ϕ4-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.

Phase Transitions in Particle Physics

“…If it can be established that the scaling behavior follows the one expected for the QCD critical point, the location of the QCD critical point can be determined by a scaling analysis. This method has been successfully applied in the Gross-Neveu model [212], see also [213] for further investigations in low energy EFTs with and without fluctuations see [214,213,215,216,217]. In particular, the scaling behavior of the location of the edge singularity has been established in [214,215,216] It is thus important to understand that these studies not only highlight different numerical strategies to calculate observables at nonvanishing chemical potential via a re-summation of the Taylor series and thus might enhance the results presented in the Section on fluctuations.…”