Multi-field galileons and higher co-dimension branes
Kurt Hinterbichler, Mark Trodden, Daniel Wesley
TL;DR
By extending the DGP-like galileon construction to higher co-dimensions, the paper derives a unique four-dimensional multi-field galileon theory controlled by a single quartic coupling, with an origin in Lovelock invariants on the brane and in the bulk. The internal SO(N) symmetry forbids odd interactions, yielding a kinetic term and a single quartic interaction in 4D that are not renormalized by quantum corrections. The authors analyze de Sitter self-accelerating solutions and show ghost conditions linked to the signs of the couplings, highlighting a tradeoff between flat-space and de Sitter stability. These results establish a geometrically grounded, quantum-mechanically stable framework for multi-field galileons with potential cosmological implications.
Abstract
In the decoupling limit, the DGP model reduces to the theory of a scalar field pi, with interactions including a specific cubic self-interaction - the galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a 5-dimensional bulk with Lovelock terms on the brane and in the bulk. We study multi-field generalizations of the galileon, and extend this probe brane view to higher co-dimensions. We derive an extremely restrictive theory of multiple galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher co-dimension bulk. We explore some properties of this theory, finding de Sitter like self accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general non-renormalization theorem: multi-field galileons are not renormalized quantum mechanically to any loop in perturbation theory.