Inverse of the String Theory KLT Kernel

Abstract

The field theory Kawai-Lewellen-Tye (KLT) kernel, which relates scattering amplitudes of gravitons and gluons, turns out to be the inverse of a matrix whose components are bi-adjoint scalar partial amplitudes. In this note we propose an analogous construction for the string theory KLT kernel. We present simple diagrammatic rules for the computation of the ${\alpha }^{\prime }$-corrected bi-adjoint scalar amplitudes that are exact in ${\alpha }^{\prime }$. We find compact expressions in terms of graphs, where the standard Feynman propagators $1/p^2$ are replaced by either $1/\sin (\pi {\alpha }^{\prime }{p}^2/2)$ or $1/\tan (\pi {\alpha }^{\prime }{p}^2/2)$, as determined by a recursive procedure. We demonstrate how the same object can be used to conveniently expand open string partial amplitudes in a BCJ basis.

25 pages, published version, Mathematica notebook attached

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Cited by in corpus (31)

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• The Kerr-Schild double copy in curved spacetime
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• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Covariant Color-Kinematics Duality
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Celestial double copy from the worldsheet
• UV considerations on scattering amplitudes in a web of theories
• Generalizations of the Double-Copy: the KLT Bootstrap
• Labelled tree graphs, Feynman diagrams and disk integrals
• Biadjoint scalar tree amplitudes and intersecting dual associahedra
• Singular Solutions in Soft Limits
• A Lie bracket for the momentum kernel
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Stokes Polytopes and Intersection Theory
• A double copy from twisted (co)homology at genus one
• A String Deformation of the Parke-Taylor Factor
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• On Polytopes and Generalizations of the KLT Relations
• Gauge and Gravity Amplitudes on the Celestial Sphere
• Lorentzian contours for tree-level string amplitudes
• KLT Factorization of Winding String Amplitudes
• Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a Circle
• KK-like relations of ${\alpha }^{\prime }$ corrections to disk amplitudes
• Positive Geometry for Stringy Scalar Amplitudes
• Twisted de Rham theory for string double copy in AdS
• A tree expansion formula of a homology intersection numbers on the configuration space ${\mathcal{M}}_{0,n}$
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• The seeds of EFT double copy