Large deformations of Tr(Φ3) and the world at infinity

A bstract The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ 3 ) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ 3 ) amplitudes under a general class of large kinematic shifts called g -vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular g -vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.