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.
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