Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD

TL;DR

This paper investigates the gravitational coupling of QCD through the trace anomaly, confirming the presence of anomaly poles in the effective action via a one-loop computation, and explores implications for dark energy models.

Contribution

It provides a complete one-loop calculation of the effective action for non-abelian gauge theories coupled to gravity, confirming the anomaly pole structure.

Findings

Confirmation of anomaly poles in the $TJJ$ correlator for quarks and gluons.

Validation of the nonlocal effective action approach to gravity-gauge coupling.

Support for infrared models of dark energy based on QCD vacuum energy behavior.

Abstract

The anomalous effective action describing the coupling of gravity to a non-abelian gauge theory can be determined by a variational solution of the anomaly equation, as shown by Riegert long ago. It is given by a nonlocal expression, with the nonlocal interaction determined by the Green's function of a conformally covariant operator of fourth order. In recent works it has been shown that this interaction is mediated by a simple pole in an expansion around a Minkowski background, coupled in the infrared in the massless fermion limit. This result relies on the local formulation of the original action in terms of two auxiliary fields, one physical scalar and one ghost, which take the role of massless composite degrees of freedom. In the gravity case, the two scalars have provided ground in favour of some recent proposals of an infrared approach to the solution of the dark energy problem, entirely based on the behaviour of the vacuum energy at the QCD phase transition. As a test of this general result, we perform a complete one-loop computation of the effective action describing the coupling of a non-abelian gauge theory to gravity. We confirm the appearance of an anomaly pole which contributes to the trace part of the $TJJ$ correlator and of extra poles in its trace-free part, in the quark and gluon sectors, describing the coupling of the energy momentum tensor ($T$) to two non abelian gauge currents ($J$).