Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms

TL;DR

This paper analyzes how brane-localized curvature terms in Randall-Sundrum models affect the scattering amplitudes of spin-2 Kaluza-Klein states, revealing modifications in high-energy behavior and implications for diffeomorphism invariance.

Contribution

It provides a detailed study of the impact of brane-localized curvature on KK graviton scattering amplitudes and their invariance properties, connecting to the DGP model and gauge theories.

Findings

Scattering amplitudes grow as ${\cal O}(s^3)$ due to brane curvature effects.

Diffeomorphism invariance is maintained for external sources but not for bulk matter.

Goldstone bosons behave as Galileons, influencing high-energy scattering behavior.

Abstract

In this paper we investigate the scattering amplitudes of spin-2 Kaluza-Klein (KK) states in Randall-Sundrum models with brane-localized curvature terms. We show that the presence of brane-localized curvature interactions modifies the properties of (4D) scalar fluctuations of the metric, resulting in scattering amplitudes of the massive spin-2 KK states which grow as ${\cal O}(s^3)$ instead of ${\cal O}(s)$. We discuss the constraints on the size of the brane-localized curvature interactions based on the consistency of the Sturm-Liouville mode systems of the spin-2 and spin-0 metric fluctuations. We connect the properties of the scattering amplitudes to the diffeomorphism invariance of the compactified KK theory with brane-localized curvature interactions. We verify that the scattering amplitudes involving brane-localized external sources (matter) are diffeomorphism-invariant, but show that those for matter localized at an arbitrary point in the bulk are not. We demonstrate that, in Feynman gauge, the spin-0 Goldstone bosons corresponding to helicity-0 states of the massive spin-2 KK bosons behave as a tower of Galileons, and that it is their interactions that produce the high-energy behavior of the scattering amplitudes. We also outline the correspondence between our results and those in the Dvali-Gabadadze-Porrati (DGP) model. In an appendix we discuss the analogous issue in extra-dimensional gauge theory, and show that the presence of a brane-localized gauge kinetic-energy term does not change the high-energy behavior of corresponding KK vector boson scattering amplitudes.