Convexity of the effective action from functional flows

TL;DR

This paper demonstrates that the convexity of the effective action can be derived from its functional flow equation using a spectral representation, with implications for physical stability analysis.

Contribution

It introduces a spectral representation approach to prove convexity from flow equations and establishes constraints for regulators that preserve convexity.

Findings

Convexity of the effective action follows from the flow equation.

Spectral representation provides a new analytical tool.

Constraints for convexity-preserving regulators are derived.

Abstract

We show that convexity of the effective action follows from its functional flow equation. Our analysis is based on a new, spectral representation. The results are relevant for the study of physical instabilities. We also derive constraints for convexity-preserving regulators within general truncation schemes including proper-time flows, and bounds for infrared anomalous dimensions of propagators.