Double Copy from the Flipped Null String

Abstract

We study the double-copy structure of tree amplitudes of the bosonic null string in the flipped vacuum. We show that its level-one vector correlator supplies the Cachazo-He-Yuan (CHY) kinematic half-integrand of the higher-derivative $(DF)^2$ gauge theory, while distinguished compact momentum-winding sectors generate the complementary Parke-Taylor factor. For factorized level-two states, the same Carrollian world-sheet produces two kinematic half-integrands and hence the symmetric double copy to the six-derivative Weyl-cubed graviton sector. Lattice sectors with common external momenta reproduce the Bern-Carrasco-Johansson (BCJ) ordering relation and the corresponding field-theory Kawai-Lewellen-Tye (KLT) representation. These results provide a direct Carrollian world-sheet origin of the double copy and point toward a current-algebra realization of the emergent color sector compatible with the $O(d,d)$ structure of the compact lattice.