  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
$G/H$, 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
correlators of nonlinear sigma model, 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.
