Semi-abelian Z-theory: NLSM+phi^3 from the open string

TL;DR

This paper explores the semi-abelian Z-theory amplitudes, showing they reproduce extended NLSM interactions with bi-adjoint scalars at leading order, and simplifies their alpha'-expansion using monodromy relations, revealing higher-derivative interactions.

Contribution

It demonstrates that semi-abelian Z-theory amplitudes reproduce extended NLSM interactions and introduces a simplified method for extracting their alpha'-expansion using monodromy relations.

Findings

Reproduction of extended NLSM amplitudes from semi-abelian Z-theory.

Simplification of permutation sums via monodromy relations.

Encoding of higher-derivative interactions and duality properties.

Abstract

We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading alpha'-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the alpha'-expansion of these amplitudes. Their alpha'-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order alpha'-corrections.