A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions

TL;DR

This paper investigates the properties of correlation functions involving conserved and anomalous currents, clarifies the unambiguous fixing of the stress tensor's improvement term, and explores the RG flow between UV and IR limits using sum rules and self-consistency checks.

Contribution

It provides a novel variational principle to fix the stress tensor's improvement ambiguity and analyzes the RG interpolation with sum rules for trace anomalies.

Findings

Unambiguous fixing of the stress tensor's improvement term.

RG flow analysis between UV and IR limits.

Consistency of results with sum rules for trace anomalies.

Abstract

I study various properties of the critical limits of correlators containing insertions of conserved and anomalous currents. In particular, I show that the improvement term of the stress tensor can be fixed unambiguously, studying the RG interpolation between the UV and IR limits. The removal of the improvement ambiguity is encoded in a variational principle, which makes use of sum rules for the trace anomalies a and a'. Compatible results follow from the analysis of the RG equations. I perform a number of self-consistency checks and discuss the issues in a large set of theories.