Abstract
We present an integration-by-parts reduction of any massless tree-level string correlator to an equivalence class of logarithmic functions, which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field-theory one and a special disk or sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL(2) weight. By applying the reduction to open bosonic or heterotic strings, we get a closed-form CHY integrand for the (DF)^{2}+Yang-Mills+ϕ^{3} theory.
Highlights
Introduction.—Recent years have seen enormous advances in understanding structures of scattering amplitudes in quantum field theories (c.f. [1,2,3]), and many crucial insights have originated from string theory
It has been realized that tree-level open- and closed-superstring amplitudes themselves can be obtained via a double copy [17]
It is well established that tree and loop CHY formulas can be derived from worldsheet models known as ambitwistor string theory [36,37], where CHY integrand is given by correlators therein
Summary
Logarithmic but usually take a more compact form and make some properties more manifest. CHY integrand from string correlator.—The double copy construction at tree level can be most conveniently expressed by KLT product of color-ordered amplitudes. ≔dμsntring where sij ≔ α0ki · kj, zij ≔ zi − zj; one can fix three punctures, e.g., ðz; zn−1; znÞ 1⁄4 ð0; 1; ∞Þ, using SLð2; RÞ redundancy, and the product in the Koba-Nielsen factor is over 1 ≤ i < j ≤ n − 1 with this fixing After stripping it off, the (reduced) string correlator In is a rational function of zs which depends on details of vertex operators. With color-ordered amplitudes in a field theory The latter is defined by a CHY formula, with integrands given by a PT factor as defined above, and a logarithmic function. 0 n on a nonminimal basis of PT factors, making further simplifications accessible
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