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The infrared structure of Nambu-Goldstone bosons

  • Ian Low
  • Zhewei Yin
Open Access
Regular Article - Theoretical Physics
  • 14 Downloads

Abstract

The construction of effective actions for Nambu-Goldstone bosons, and the nonlinear sigma model, usually requires a target coset space G/H. Recent progresses uncovered a new formulation using only IR data without reference to the broken group G in the UV, by imposing the Adler’s zero condition, which can be seen to originate from the superselection rule in the space of degenerate vacua. The IR construction imposes a nonlinear shift symmetry on the Lagrangian to enforce the correct single soft limit amid constraints of the unbroken group H. We present a systematic study on the consequence of the Adler’s zero condition in correlation functions of nonlinear sigma models, by deriving the conserved current and the Ward identity associated with the nonlinear shift symmetry, and demonstrate how the old-fashioned current algebra emerges. The Ward identity leads to a new representation of on-shell amplitudes, which amounts to bootstrapping the higher point amplitudes from lower point amplitudes and adding new vertices to satisfy the Adler’s condition. The IR perspective allows one to extract Feynman rules for the mysterious extended theory of biadjoint cubic scalars residing in the subleading single soft limit, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. In addition, we present the subleading triple soft theorem in the nonlinear sigma model and show that it is also controlled by on-shell amplitudes of the same extended theory as in the subleading single soft limit.

Keywords

Effective Field Theories Sigma Models Spontaneous Symmetry Breaking Scattering Amplitudes 

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) 2018

Authors and Affiliations

  1. 1.Department of Physics and AstronomyNorthwestern UniversityEvanstonU.S.A.
  2. 2.High Energy Physics DivisionArgonne National LaboratoryArgonneU.S.A.
  3. 3.Theoretical Physics DepartmentCERNGeneva 23Switzerland

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