Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes

Abstract

We analyze the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the KK gravitational Goldstone bosons in the compactified 5d General Relativity (GR). Using a general $R_{\xi }$ gauge-fixing, we study the geometric Higgs mechanism for the massive spin-2 KK gravitons. We newly propose and prove a Gravitational Equivalence Theorem (GRET) to connect the scattering amplitudes of longitudinal KK gravitons to that of the KK gravitational Goldstone bosons, which formulates the geometric gravitational Higgs mechanism at the scattering $S$-matrix level. We demonstrate that the GRET provides a general energy-cancellation mechanism guaranteeing the $N$-point longitudinal KK graviton scattering amplitudes to have their leading energy dependence cancelled down by a large power factor of $E^{2N}$ ($N\ge 4$) up to any loop order. We propose an extended double-copy approach to construct the massive KK graviton (Goldstone) amplitudes from the KK gauge boson (Goldstone) amplitudes. With these we establish a new correspondence between the two types of energy cancellations in the four-point longitudinal KK amplitudes at tree level: $E^4\to E^0$ in the KK gauge theory and $E^{10}\to E^2$ in the KK GR theory.

arXiv comment9 pages (+Supplemental Material), including exact KK double-copy of both LO + NLO. This Letter is the companion of the recent systematic long paper in PRD 105 (2022) 084005 [arXiv:2106.04568]

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• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
• Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions
• Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms