NLSM ⊂ Tr(ϕ^3)

Scattering amplitudes for the simplest theory of colored scalar particles - the Tr(ϕ^3) theory - have recently been the subject of active investigations. In this letter we describe an unanticipated wider implication of this work: the Tr(ϕ^3) theory secretly contains Non-linear Sigma Model (NLSM) amplitudes to all loop orders. At tree level, the NLSM amplitudes are obtained from Tr(ϕ^3) amplitudes by a unique shift of kinematic variables, guaranteeing the correct pole structure, factorization, and the Adler zero. Remarkably, essentially the same shifts for tree and loop kinematic variables of the planar Tr(ϕ^3) integrand produce the planar loop integrand of the NLSM with correct poles and residues, exhibiting the Adler zero for the integrated amplitudes. Similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr(ϕ^3) scalars.