  The low energy effective action of gravity in any even dimension generally
acquires non-local terms associated with the trace anomaly, generated by the
quantum fluctuations of massless fields. The local auxiliary field description
of this effective action in four dimensions requires two additional scalar
fields, not contained in classical general relativity, which remain relevant at
macroscopic distance scales. The auxiliary scalar fields depend upon boundary
conditions for their complete specification, and therefore carry global
information about the geometry and macroscopic quantum state of the
gravitational field. The scalar potentials also provide coordinate invariant
order parameters describing the conformal behavior and divergences of the
stress tensor on event horizons. We compute the stress tensor due to the
anomaly in terms of its auxiliary scalar potentials in a number of concrete
examples, including the Rindler wedge, the Schwarzschild geometry, and de
Sitter spacetime. In all of these cases, a small number of classical order
parameters completely determine the divergent behaviors allowed on the horizon,
and yield qualitatively correct global approximations to the renormalized
expectation value of the quantum stress tensor.
