Bootstrapping the String Kawai-Lewellen-Tye Kernel

We show that double-copy maps for amplitudes in effective field theory are severely constrained at four points by self-consistency and locality at six points. The resulting double-copy kernel depends only on two parameters as well as a specific symmetric function in s, t, u and interpolates between the original Kawai-Lewellen-Tye (KLT) string double copy and the open and closed string period integrals. Amplitudes double copied with this map must obey either the string monodromy relations or the field theory Kleiss-Kuijf (KK) and Bern, Carrasco, and Johansson (BCJ) relations; there are no other options. Our construction elucidates the "single-valued projection" property of the Riemann zeta-function values for the four-point string theory double copy.