Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories

TL;DR

This paper demonstrates how residual symmetries in warped five-dimensional gravitational theories lead to Equivalence theorems, simplifying the calculation of spin-2 scattering amplitudes and clarifying their energy growth behavior.

Contribution

It establishes a connection between residual diffeomorphism symmetries and Equivalence theorems, providing explicit calculations and power-counting methods for spin-2 Kaluza-Klein states.

Findings

Scattering amplitudes of helicity-0 and helicity-1 states equal Goldstone boson amplitudes at leading order.

Derived Ward identities enable transparent power-counting of amplitudes.

Amplitudes grow no faster than O(s), explaining cancellations in unitary gauge.

Abstract

Building on work by Hang and He, we show how the residual five-dimensional diffeomorphism symmetries of compactified gravitational theories with a warped extra dimension imply Equivalence theorems which ensure that the scattering amplitudes of helicity-0 and helicity-1 spin-2 Kaluza-Klein states equal (to leading order in scattering energy) those of the corresponding Goldstone bosons present in the `t-Hooft-Feynman gauge. We derive a set of Ward identities that lead to a transparent power-counting of the scattering amplitudes involving spin-2 Kaluza-Klein states. We explicitly calculate these amplitudes in terms of the Goldstone bosons in the Randall-Sundrum model, check the correspondence to previous unitary-gauge computations, and demonstrate the efficacy of `t-Hooft-Feynman gauge for accurately computing amplitudes for scattering of the spin-2 states both among themselves and with matter. Power-counting for the Goldstone boson interactions establishes that the scattering amplitudes grow no faster than $O(s)$, explaining the origin of the behavior previously shown to arise from intricate cancellations between different contributions to these scattering amplitudes in unitary gauge. We describe how our results apply to more general warped geometries, including models with a stabilized extra dimension. In an appendix we explicitly identify the symmetry algebra of the residual 5D diffeomorphisms of a Randall-Sundrum extra-dimensional theory.