  We extend the effective field theory (EFT) formalism for gravitational
radiation from a binary system of compact objects to the case of extended
objects. In particular, we study the EFT for a binary system consisting of two
infinitely-long cosmic strings with small velocity and small spatial
substructure, or "wiggles". The complexity of the system requires the
introduction of two perturbative expansion parameters, constructed from the
velocity and size of the wiggles, in contrast with the point particle case, for
which a single parameter is sufficient. This further requires us to assign new
power counting rules in the system. We integrate out the modes corresponding to
potential gravitons, yielding an effective action for the radiation gravitons.
We show that this action describes a changing quadrupole, sourced by the
bending modes of the string, which in turn generates gravitational waves. We
study the ultraviolet divergences in this description, and use them to obtain
the classical renormalization group flow of the string tension in such a
setting.
