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The anomalous effective action describing the coupling of gravity to anon-abelian gauge theory can be determined by a variational solution of theanomaly equation, as shown by Riegert long ago. It is given by a nonlocalexpression, with the nonlocal interaction determined by the Green's function ofa conformally covariant operator of fourth order. In recent works it has beenshown that this interaction is mediated by a simple pole in an expansion arounda Minkowski background, coupled in the infrared in the massless fermion limit.This result relies on the local formulation of the original action in terms oftwo auxiliary fields, one physical scalar and one ghost, which take the role ofmassless composite degrees of freedom. In the gravity case, the two scalarshave provided ground in favour of some recent proposals of an infrared approachto the solution of the dark energy problem, entirely based on the behaviour ofthe vacuum energy at the QCD phase transition. As a test of this generalresult, we perform a complete one-loop computation of the effective actiondescribing the coupling of a non-abelian gauge theory to gravity. We confirmthe 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 andgluon sectors, describing the coupling of the energy momentum tensor ($T$) totwo non abelian gauge currents ($J$).

Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD