Kinematic sum rules for trace anomalies

TL;DR

This paper develops a method to derive sum rules for trace anomalies in quantum field theories, connecting UV and IR fixed points through flow integrals of stress tensor correlators, with implications for RG flow irreversibility.

Contribution

It introduces a general procedure to generate sum rules for trace anomalies a and a', applicable to all renormalizable quantum field theories, including non-unitary cases.

Findings

Universal flow invariants for Delta a are obtained.

Sum rules connect UV and IR fixed points via stress tensor correlators.

The method can be extended to derive sum rules for the trace anomaly c.

Abstract

I derive a procedure to generate sum rules for the trace anomalies a and a'. Linear combinations of Delta a = a_UV-a_IR and Delta a' = a'_UV-a'_IR are expressed as multiple flow integrals of the two-, three- and four-point functions of the trace of the stress tensor. Eliminating Delta a', universal flow invariants are obtained, in particular sum rules for Delta a. The formulas hold in the most general renormalizable quantum field theory (unitary or not), interpolating between UV and IR conformal fixed points. I discuss the relevance of these sum rules for the issue of the irreversibility of the RG flow. The procedure can be generalized to derive sum rules for the trace anomaly c.