  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 ($J$).
