Constraining higher-spin S-matrices

Abstract

There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial S-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg’s soft theorem — a direct consequence of the Lorentz invariance of the S-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation — a representation originated from twistor theory, we show that Weinberg’s soft theorem can be evaded and non-trivial higher-spin S-matrix is possible. In particular, we show that Weinberg’s soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the S-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is a charge conservation law.