  We present the first complete (i.e., ambiguity-free) derivation of the
equations of motion of two non-spinning compact objects up to the 4PN order,
based on the Fokker action of point particles in harmonic coordinates. The last
ambiguity parameter is determined from first principle, by resorting to a
matching between the near zone and far zone fields, and a consistent
computation of the 4PN tail effect in d dimensions. Dimensional regularization
is used throughout for treating IR divergences appearing at 4PN order, as well
as UV divergences due to the model of point particles describing compact
objects.
