TY - JOUR

T1 - The infrared structure of Nambu-Goldstone bosons

AU - Low, Ian

AU - Yin, Zhewei

N1 - Funding Information:
This work is supported in part by the U.S. Department of Energy under contracts No. DE-AC02-06CH11357 and No. DE-SC0010143. We thank John R. Ellis for bringing ref. [10] to our attention.
Publisher Copyright:
© 2018, The Author(s).

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - Effective Field Theories

KW - Scattering Amplitudes

KW - Sigma Models

KW - Spontaneous Symmetry Breaking

UR - http://www.scopus.com/inward/record.url?scp=85054681056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054681056&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2018)078

DO - 10.1007/JHEP10(2018)078

M3 - Article

AN - SCOPUS:85054681056

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 78

ER -