Convexity of the effective action from functional flows
  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. 
Daniel F. Litim, Jan M. Pawlowski, Lautaro Vergara