Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes

Understand

It has recently been shown explicitly that the high-energy scattering amplitude of the longitudinal modes of massive spin-2 Kaluza Klein states in compactified 5-dimensional gravity, which would naively grow like O(s^5), grow only like O(s).

• Since the individual contributions to these amplitudes do grow like O(s^5), the required cancellations between these individual contributions result from intricate relationships between the masses of these states and their couplings.
• Here we report the explicit form of these sum-rule relationships which ensure the necessary cancellations for elastic scattering of spin-2 Kaluza Klein states in a Randall-Sundrum model.
• We consider an Anti-de-Sitter space of arbitrary curvature, including the special case of a toroidal compactification in which the curvature vanishes.