String amplitudes from QFT amplitudes and vice versa


Author: Song He, Fei Teng and Yong Zhang

Preprint number: UUITP-58/18

We present an integration-by-part 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/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/heterotic strings, we get a closed-form CHY integrand for the $DF^2+\text{YM}+\phi^3$ theory.