Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy

Abstract

We study the scattering amplitudes of massive Kaluza-Klein (KK) states of open and closed bosonic strings under toroidal compactification. We analyze the structure of vertex operators for the KK strings and derive an extended massive KLT-like relation which connects the $N$-point KK closed-string amplitude to the products of two KK open-string amplitudes at tree level. Taking the low energy field-theory limit of vanishing Regge slope, we derive double-copy construction formula of the $N$-point massive KK graviton amplitude from the sum of proper products of the corresponding KK gauge boson amplitudes. Then, using the string-based massive double-copy formula, we derive the exact tree-level four-point KK gauge boson amplitudes and KK graviton amplitudes, which fully agree with those given by the KK field-theory calculations. With these, we give an explicit prescription on constructing the exact four-point KK graviton amplitudes from the sum of proper products of the corresponding color-ordered KK gauge boson amplitudes. We further analyze the string-based double-copy construction of five-point and six-point scattering amplitudes of massive KK gauge bosons and KK gravitons.

arXiv comment41 pages, JHEP version, only minor refinements, references added

References in corpus (34)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Resummation of Massive Gravity
• New Relations for Gauge-Theory Amplitudes
• Generalization of the Fierz-Pauli Action
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• The Momentum Kernel of Gauge and Gravity Theories
• On the Unification Problem in Physics
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Unitarity of Compactified Five Dimensional Yang-Mills Theory
• The Duality Between Color and Kinematics and its Applications
• Unitarity of the Higher Dimensional Standard Model
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Massive Gravity from Double Copy
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Massive Spin-2 Scattering Amplitudes in Extra-Dimensional Theories
• Higgsless Deconstruction Without Boundary Condition
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as $\mathcal{O}(s)$
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• KLT Factorization of Winding String Amplitudes
• Massive Covariant Colour-Kinematics in 3D

Cited by in corpus (10)

• Off-Shell Color-Kinematics Duality for Chern-Simons
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• KLT Factorization of Nonrelativistic String Amplitudes
• Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes
• 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
• The seeds of EFT double copy
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions