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In this paper we derive the tree-level S-matrix of the effective theory ofGoldstone bosons known as the non-linear sigma model (NLSM) from string theory.This novel connection relies on a recent realization of tree-levelopen-superstring S-matrix predictions as a double copy of super-Yang-Millstheory with Z-theory --- the collection of putative scalar effective fieldtheories encoding all the alpha'-dependence of the open superstring. Here weidentify the color-ordered amplitudes of the NLSM as the low-energy limit ofabelian Z-theory. This realization also provides natural higher-derivativecorrections to the NLSM amplitudes arising from higher powers of alpha' in theabelian Z-theory amplitudes, and through double copy also to Born-Infeld andVolkov-Akulov theories. The Kleiss-Kuijf and Bern-Carrasco-Johansson relationsobeyed by Z-theory amplitudes thereby apply to all alpha'-corrections of theNLSM. As such we naturally obtain a cubic-graph parameterization for theabelian Z-theory predictions whose kinematic numerators obey the dualitybetween color and kinematics to all orders in alpha'.

Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string