Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models


Authors: Laurentiu Rodina, Zhewei Yin

Preprint number: UUITP-10/21

Abstract: We generalize soft theorems of the nonlinear sigma model beyond the O(p^2) amplitudes and the coset of SU(N)×SU(N)/SU(N). We first discuss the flavor ordering of the amplitudes for the Nambu-Goldstone bosons of a general symmetry group representation,  so that we can reinterpret the known O(p^2) single soft theorem for SU(N)×SU(N)/SU(N) in the context of a general group representation. We then investigate the special case of the fundamental representation of SO(N), where a special flavor ordering of the "pair basis" is available. We provide novel amplitude relations and a Cachazo-He-Yuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation to O(p^4), where for at least two specific choices of the O(p^4) operators, the leading non-vanishing pieces can be interpreted as new extended theory amplitudes involving bi-adjoint scalars, and the corresponding soft factors are the same as at O(p^2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by the O(p^2) Lagrangian, while any possible corrections to the subleading part are determined by the O(p^4) Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.