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

TL;DR

This paper connects string theory and effective field theories by deriving NLSM amplitudes from open superstring theory, revealing higher-derivative corrections and duality properties through abelian Z-theory.

Contribution

It identifies NLSM amplitudes as the low-energy limit of abelian Z-theory and extends the double copy framework to include alpha'-dependent corrections.

Findings

NLSM amplitudes are derived from abelian Z-theory.

Higher-derivative alpha' corrections are naturally incorporated.

Color-kinematics duality holds to all orders in alpha'.

Abstract

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