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

  • John Joseph M. Carrasco
  • Carlos R. Mafra
  • Oliver SchlottererEmail author
Open Access
Regular Article - Theoretical Physics

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 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.

Keywords

Scattering Amplitudes Sigma Models Superstrings and Heterotic Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • John Joseph M. Carrasco
    • 1
    • 2
  • Carlos R. Mafra
    • 3
    • 2
  • Oliver Schlotterer
    • 4
    Email author
  1. 1.Institut de Physique Théorique, CEA-SaclayGif-sur-Yvette cedexFrance
  2. 2.Institute for Advanced Study, School of Natural SciencesPrincetonU.S.A.
  3. 3.STAG Research Centre and Mathematical SciencesUniversity of SouthamptonSouthamptonU.K.
  4. 4.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutPotsdamGermany

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