On extended supersymmetry of 4d Galileons and 3-brane effective actions

Abstract

We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous $$ \mathcal{N} $$ N = 1 results. Assuming spins ≤ 1, we prove that there exists no $$ \mathcal{N} $$ N = 4 supersymmetric extension of 4d Galileons with a single vector multiplet. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the α′-expansion of the abelian open superstring amplitude. For $$ \mathcal{N} $$ N = 2 Galileons, we show that the complex scalar Z = ϕ + iχ of the vector supermultiplet cannot have ϕ and χ both enjoy enhanced shift symmetry; instead, χ can at best be an R-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with $$ \mathcal{N} $$ N = 2 supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of $$ \mathcal{N} $$ N = 2 supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric couplings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs. the Swampland.