  Stress-energy correlation functions in a general Conformal Field Theory (CFT)
in four dimensions are described in a fully covariant approach, as metric
variations of the quantum effective action in an arbitrary curved space
background field. All Conservation, Trace and Conformal Ward Identities (CWIs),
including contact terms, are completely fixed in this covariant approach. The
Trace and CWIs are anomalous. Their anomalous contributions may be computed
unambiguously by metric variation of the exact 1PI quantum effective action
determined by the conformal anomaly of $\left\langle T^{\mu\nu}\right\rangle$
in $d = 4$ curved space. This action implies the existence of massless
propagator poles in three and higher point correlators of $T^{\mu\nu}$ . The
metric variations of the anomaly effective action in its local form in terms of
a scalar conformalon field are carried out explicitly for the case of the
correlator of three CFT stress-energy tensors, and the result is shown to
coincide with the algebraic reconstruction of $\left\langle TTT\right\rangle$
from its transverse, tracefree parts, determined independently by the solution
of the CWIs in d dimensional flat space in the momentum representation. This
demonstrates that the specific analytic structure and massless poles predicted
by the general curved space anomaly effective action are in fact a necessary
feature of the exact solution of the anomalous CWIs in any $d = 4$ CFT.
