Twisted de Rham theory for string double copy in AdS

Abstract

This work is motivated by the recent evidence for a double-copy relationship between open- and closed-string amplitudes in Anti-de Sitter (AdS) space. At present, the evidence has the form of a double-copy relation for string-amplitude building blocks, which are combined using the multiple-polylogarithm (MPL) generating functions. These generate MPLs relevant for all-order AdS curvature corrections of four-point string amplitudes. In this paper, we prove this building-block double copy using a new, noncommutative version of twisted de Rham theory. In flat space, the usual twisted de Rham theory is already known to be a natural framework to describe the Kawai-Lewellen-Tye (KLT) double-copy map from open- to closed-string amplitudes, in which the KLT kernel can be computed from the intersections of the open-string amplitude integration contours. We formulate twisted de Rham theory for noncommutative-ring-valued differential forms on complex manifolds and use it to derive the intersection number of two open-string contours, which are closed in the noncommutative twisted homology sense. The inverse of this intersection number is precisely the AdS double-copy kernel for the four-point open- and closed-string generating functions.

29 pages + appendix + refs, 4 figures; v3 minor improvements, journal version

References in corpus (35)

• New Relations for Gauge-Theory Amplitudes
• Harmonic Polylogarithms
• 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
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Double copy for massive quantum particles with spin
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Aspects of Scattering Amplitudes and Moduli Space Localization
• Gravity and Yang-Mills Amplitude Relations
• Proof of Gravity and Yang-Mills Amplitude Relations
• Gluon Scattering in AdS from CFT
• All order alpha'-expansion of superstring trees from the Drinfeld associator
• On duality of color and kinematics in (A)dS momentum space
• Monodromy Relations in Higher-Loop String Amplitudes
• Higher-loop amplitude monodromy relations in string and gauge theory
• The AdS Virasoro-Shapiro Amplitude
• Double Copy Relation for AdS
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• AdS Virasoro-Shapiro from single-valued periods
• AdS Virasoro-Shapiro from dispersive sum rules
• Tree-level amplitudes from the pure spinor superstring
• Inverse of the String Theory KLT Kernel
• Closed strings as single-valued open strings: A genus-zero derivation
• Intersection numbers of twisted cycles and the correlation functions of the conformal field theory II
• Monodromy relations from twisted homology
• One-loop monodromy relations on single cuts
• Loop amplitudes monodromy relations and color-kinematics duality
• The AdS Veneziano amplitude at small curvature
• Coaction and double-copy properties of configuration-space integrals at genus zero
• A double copy from twisted (co)homology at genus one
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory