TY - JOUR

T1 - Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

AU - Low, Ian

AU - Yin, Zhewei

N1 - Publisher Copyright:
© 2018 authors. Published by the American Physical Society. Funded by SCOAP.

PY - 2018/2/5

Y1 - 2018/2/5

N2 - We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

AB - We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

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U2 - 10.1103/PhysRevLett.120.061601

DO - 10.1103/PhysRevLett.120.061601

M3 - Article

C2 - 29481273

AN - SCOPUS:85041794659

SN - 0031-9007

VL - 120

JO - Physical review letters

JF - Physical review letters

IS - 6

M1 - 061601

ER -