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

John Joseph Carrasco, Carlos R. Mafra, Oliver Schlotterer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


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 pre-dictions as a double copy of super-Yang-Mills theory with Z-theory — the collection of putative scalar effective field theories encoding all the α-expansion of the open super-string. 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 α in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The amplitude relations due to Kleiss-Kuijf as well as Bern, Johansson and one of the current authors obeyed by Z-theory amplitudes thereby apply to all α-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 α.

Original languageEnglish (US)
Article number93
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 1 2017


  • Scattering Amplitudes
  • Sigma Models
  • Superstrings and Heterotic Strings

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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