Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2106.04568

Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy

Yan-Feng Hang·Hong-Jian He
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_ξ$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

Explore related subjects

hep-thgr-qchep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yan-Feng Hang, Hong-Jian He. 2022-07-28. Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy. https://doi.org/10.1103/physrevd.105.084005

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th↗
arXiv2026

Criticality of ISCOs and AdS/CFT

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $γ$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{Δ_H}$ to $γ$ in the dual CFT, and dsicuss the implications of our results.

hep-th↗
arXiv2026

Constraining F-theory Model Building with QCD Axions

In this paper, we investigate axion physics in 4D F-theory MSSM models. We derive the axion coupling term with QCD gauge fields and the axion potential from a top-down perspective, from both IIB superstring and the dual M-theory picture. For the explicit geometric model, we employ the "quadrillion" landscape of 4D F-theory models with the exact Standard Model chiral spectrum, and study simple base threefolds such as $\mathbb{P}^3$, $\mathbb{P}^1\times\mathbb{P}^2$, the generalized Hirzebruch threefold $\tilde{\mathbb{F}}_3$ and $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$. We derive exclusion constraints on the Kähler moduli space of the base threefold from the CP violation angle, the Standard Model gauge coupling constants and the stretched Kähler cone condition. We find stringent constraints on the set of base divisors that should be rigid or rigidified by the inclusion of flux. For the allowed regions of the parameter space, we estimate the typical mass of detectable QCD axions to be around $10^{-9}$eV, and the axion decay constant to be around $f_a\sim 10^{15}$GeV.

hep-th↗