Anomalies, Unitarity and Quantum Irreversibility

TL;DR

This paper investigates the trace anomaly in external gravity, establishing a connection between unitarity, RG flow irreversibility, and the a-function, supported by perturbative tests in various quantum field theories.

Contribution

It demonstrates that the total RG flows of the anomaly coefficients a and a' are equal, allowing the removal of the a'-ambiguity and clarifying the nature of RG irreversibility.

Findings

The a'-ambiguity can be eliminated by identifying a' with a.

The a-function decreases monotonically along RG flows, indicating irreversibility.

Perturbative tests in QCD, supersymmetric QCD, QED, and phi^4 theory support the theoretical predictions.

Abstract

The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and Box R, with coefficients, properly normalized, called c, a and a', the latter being ambiguously defined by an additive constant. Considerations about unitarity and positivity properties of the induced actions allow us to show that the total RG flows of a and a' are equal and therefore the a'-ambiguity can be consistently removed through the identification a'=a. The picture that emerges clarifies several long-standing issues. The interplay between unitarity and renormalization implies that the flux of the renormalization group is irreversible. A monotonically decreasing a-function interpolating between the appropriate values is naturally provided by a'. The total a-flow is expressed non-perturbatively as the invariant (i.e. scheme-independent) area of the graph of the beta function between the fixed points. We test this prediction to the fourth loop order in perturbation theory, in QCD with Nf ~< 11/2 Nc and in supersymmetric QCD. There is agreement also in the absence of an interacting fixed point (QED and phi^4-theory). Arguments for the positivity of a are also discussed.