Symmetries for Galileons and DBI scalars on curved space

Abstract

We introduce a general class of four-dimensional effective field theories which include curved space Galileons and DBI theories possessing nonlinear shift-like symmetries. These effective theories arise from purely gravitational actions for 3-branes probing higher dimensional spaces. In the simplest case of a Minkowski brane embedded in a higher dimensional Minkowski background, the resulting four-dimensional effective field theory is the Galileon one, with its associated Galilean symmetry and second order equations. However, much more general structures are possible. We construct the general theory and explicitly derive the examples obtained from embedding maximally symmetric branes in maximally symmetric ambient spaces. Among these are Galileons and DBI theories with second order equations that live on de Sitter or anti-de Sitter space, and yet retain the same number of symmetries as their flat space counterparts, symmetries which are highly non-trivial from the 4d point of view. These theories have a rich structure, containing potentials for the scalar fields, with masses protected by the symmetries. These models may prove relevant to the cosmology of both the early and late universe.

Beyond the cosmological standard model

“…This theory has been extensively studied in many contexts including inflation [142,440,443] and late time acceleration. The DBI theory arises naturally as the world volume theory of a brane probing a higher-dimensional space and therefore inherits the isometries of the target space as global symmetries [484][485][486][487].…”

“…By considering a 3-brane probing a non-dynamical bulk, the actions for galileons, conformal galileons and covariant galileons appear as the non-relativistic limit of world-volume and bulk Lovelock invariants [584]. This probe brane construction has been greatly generalized-it has been applied to all cases of maximally symmetric branes probing maximally symmetric bulks [485][486][487], to higher codimensions [570,574] and to cosmological backgrounds [585], each leading to novel scalar theories. See [258] for a review of these extensions.…”

Inflation and String Theory

“…We see that dilatations and SCTs shift the field value and its gradient, respectively. After gauge fixing, these transformations of φ become global symmetries [715], which constrain the form of the action. First, we note that the unbroken four-dimensional Lorentz symmetry and the nonlinearly realized dilatation symmetry (5.110) imply…”

DBI from gravity

“…For simplicity we will start with the co-dimension 1 case, which was described in [18,19], but the construction can be extended to higher co-dimension straightforwardly [20][21][22].…”