DBI and the Galileon reunited

TL;DR

The article presents a unified four-dimensional EFT framework in which DBI-like and Galileon-like scalar interactions arise as a brane-position modulus in a five-dimensional bulk. By leveraging Lovelock invariants and their Gibbons-Hawking-York boundary terms, it derives a simple brane action that naturally yields the Galileon, Conformal Galileon, and their relativistic generalizations while remaining well-posed at the level of the Cauchy problem. The authors show how, in various limits (nonrelativistic Galileon, AdS DBI, and conformal reductions), the expected interactions reappear and how gravity couples covariantly, recovering the Covariant Galileon with correct nonminimal couplings. The higher-dimensional perspective clarifies the symmetry structure, provides recursion relations among induced operators, and offers a natural path toward UV completion and phenomenological applications of IR-modified gravity models.

Abstract

We derive the relativistic generalization of the Galileon, by studying the brane position modulus of a relativistic probe brane embedded in a five- dimensional bulk. In the appropriate Galilean contraction limit, we recover the complete Galileon generalization of the DGP decoupling theory and its conformal extension. All higher order interactions for the Galileon and its relativistic generalization naturally follow from the brane tension, induced curvature, and the Gibbons-Hawking-York boundary terms associated with all bulk Lovelock invariants. Our approach makes the coupling to gravity straightforward, in particular allowing a simple rederivation of the nonmini- mal couplings required by the Covariant Galileon. The connection with the Lovelock invariants makes the well-defined Cauchy problem manifest, and gives a natural unification of four dimensional effective field theories of the DBI type and the Galileon type.