Generalizing Galileons

TL;DR

The work investigates two generalizations of Galileon theories: multi-field Galileons arising from higher-codimension branes and fully covariant Galileons on curved spaces. It shows that multi-Galileons emerge with an internal $\mathrm{SO}(N)$ symmetry from brane embeddings, with a unique 4D structure consisting of a kinetic term ${\cal L}_2$ and a quartic interaction ${\cal L}_4$ that maintain second-order equations and enjoy a non-renormalization property. It then develops covariant Galileons by moving to a dynamical brane in a curved bulk, deriving a set of curved-space Galileon terms ${\cal L}_1$–${\cal L}_5$ whose symmetry protection yields curvature-induced potentials with masses tied to the background radius. Overall, the paper connects 4D Galileon-like theories to higher-dimensional brane constructions, suggesting new cosmological and particle-physics applications and pointing to possible string-theory embeddings as a future direction.

Abstract

The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a 3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief review article, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from co-dimension greater than one flat branes embedded in a flat background - the multiGalileons - and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.