Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

Physical Review Letters
Ian Low, Zhewei Yin

Abstract

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.

References

Nov 8, 2014·Physical Review Letters·Freddy CachazoEllis Ye Yuan
Jul 22, 2015·Physical Review Letters·Clifford CheungJaroslav Trnka
Feb 13, 2016·Physical Review Letters·Clifford CheungJaroslav Trnka
Apr 8, 2017·Physical Review Letters·Clifford Cheung, Chia-Hsien Shen

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Citations

Jun 5, 2018·Physical Review Letters·Yuta Hamada, Gary Shiu
Jan 13, 2019·Physical Review Letters·Da LiuZhewei Yin
Mar 9, 2019·Physical Review Letters·Laurentiu Rodina
Apr 4, 2020·Physical Review Letters·Karol KampfJaroslav Trnka

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