On the supersymmetrization of Galileon theories in four dimensions

We use on-shell amplitude techniques to study the possible N = 1 supersymmetrizations of Galileon theories in 3 + 1 dimensions, both in the limit of decoupling from DBI and without. Our results are that (1) the quartic Galileon has a supersymmetrization compatible with Galileon shift symmetry (phi -> phi + c + b(mu)x(mu)) for the scalar sector and a constant shift symmetry (psi -> psi + xi) for the fermion sector, and it is unique at least at 6th order in fields, but possibly not beyond; (2) the enhanced special Galileon symmetry is incompatible with supersymmetry; (3) there exists a quintic Galileon with a complex scalar preserving Galileon shift symmetry; (4) one cannot supersymmetrize the cubic and quintic Galileon while preserving the Galileon shift symmetry for the complex scalar; and (5) for the quartic and quintic Galileon, we present evidence for a supersymmetrization in which the real Galileon scalar is partnered with an R-axion to form a complex scalar which only has an ordinary shift symmetry. (C) 2018 The Author(s). Published by Elsevier B.V.