String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations

Abstract

We further elaborate on the general construction proposed in arXiv:1812.03369, which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding $(DF{)}^2+\mathrm{YM}+{\varphi }^3$ amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

42 pages, 4 captioned figures; v2: published version; ancillary Mathematica notebook implements the IBP algorithm described in the paper

References in corpus (31)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Scattering Amplitudes from Intersection Theory
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New Relations for Einstein-Yang-Mills Amplitudes
• Heterotic and bosonic string amplitudes via field theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Scattering Equations and String Theory Amplitudes
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Current Algebra on the Torus
• Unraveling conformal gravity amplitudes
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Closed strings as single-valued open strings: A genus-zero derivation
• New Formulas for Amplitudes from Higher-Dimensional Operators
• String amplitudes from field-theory amplitudes and vice versa
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Labelled tree graphs, Feynman diagrams and disk integrals
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• Connecting the ambitwistor and the sectorized heterotic strings
• A graphic approach to gauge invariance induced identity
• String-Like Dual Models for Scalar Theories
• A String Deformation of the Parke-Taylor Factor

Cited by in corpus (23)

• 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
• Celestial double copy from the worldsheet
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Scattering Massive String Resonances through Field-Theory Methods
• Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• On the New Factorizations of Yang-Mills Amplitudes
• Bosonic sectorized strings and the $(DF{)}^2$ theory
• Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes
• Basis decompositions of genus-one string integrals
• UV consistency conditions for CHY integrands
• Advanced tools for basis decompositions of genus-one string integrals
• Form factors from string amplitudes
• CHY Theory for Several Fields
• Superstring amplitudes meet surfaceology