Emergence of String Monodromy in Effective Field Theory.

We demonstrate that when the field theory Kleiss-Kuijf and Bern-Carrasco-Johansson relations are imposed on one color ordering of general local bi-adjoint scalar effective field theories, the string monodromy relations must be obeyed by the other color ordering. This is a surprising example of an open string world-sheet property appearing in a purely field theoretic context. As part of the derivation, we show that nonlinear relations among the four-point Wilson coefficients arise from imposing linear symmetries on the six-point amplitude via factorization.

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.