Bootstrapping the String KLT Kernel

TL;DR

This paper characterizes the most general 4-point double-copy map in effective field theory, revealing its dependence on string parameters and its relation to string monodromy and field theory relations, with a closed-form interpolation.

Contribution

It introduces a generalized 4-point double-copy map with two parameters, unifying string and field theory double-copy constructions, and clarifies the single-valued projection property.

Findings

The generalized map is defined by a two-parameter function symmetric in $s,t,u$.

It interpolates between KLT string double-copy and string period integrals.

The map's form is constrained by bootstrap analysis and string/field theory relations.

Abstract

We show that a generalized version of the 4-point string theory KLT double-copy map is the most general solution to the minimal-rank double-copy bootstrap in effective field theory. This follows from significant restrictions of the 4-point map resulting from the 6-point bootstrap analysis. The generalized 4-point double-copy map is defined by a function with only two parameters times a simple function that is symmetric in $s,t,u$. The two parameters can be interpreted as independent choices of $\alpha'$, one for each of the two sets of amplitudes double-copied with the map. Specifically, each of those two sets of amplitudes must obey either the string monodromy relations or the field theory KK & BCJ relations; there are no other options. We propose a closed form of the new double-copy map that interpolates between the original KLT string double-copy and the open & closed string period integrals. The construction clarifies the "single-valued projection" property of the Riemann zeta-function values for the 4-point string theory double copy.