Zamolodchikov's C-theorem and phase transitions

TL;DR

This paper explores the extension of Zamolodchikov's C-theorem within different renormalization group frameworks and its connection to phase transitions in finite temperature quantum field theory, highlighting the role of the effective action's properties.

Contribution

It proposes generalizations of the C-theorem in RG approaches and links the theorem to phase transitions and effective action properties in finite temperature QFT.

Findings

Zamolodchikov's theorem relates to phase transitions in finite temperature QFT.

The paper discusses the holomorphic property of the Wilson effective action.

Connections between C-theorem generalizations and RG flows are analyzed.

Abstract

We discuss the possibility of generalizing some aspects of the C-theorem within two different approaches, the conventional RG and the Wilson RG flows. We show that the original Zamolodchikov's theorem is related to the existence of the phase transitions in finite temperature QFT. We present some arguments related to the holomorphic property of the low energy Wilson effective action.