We study the structure of the flat space wavefunctional in scalar field
theories with nonlinearly realized symmetries. These symmetries imply soft
theorems that are satisfied by wavefunction coefficients in the limit where one
of the external momenta is scaled to zero. After elucidating the structure of
these soft theorems in the nonlinear sigma model, Dirac-Born-Infeld, and
galileon scalar theories, we combine them with information about the
singularity structure of the wavefunction to bootstrap the wavefunction
coefficients of these theories. We further systematize this construction
through two types of recursion relations: one that utilizes the flat space
scattering amplitude plus minimal information about soft limits, and an
alternative that does not require amplitude input, but does require subleading
soft information.
