Classification of four-point local gluon S-matrices

A bstract In this paper, we classify four-point local gluon S-matrices in arbitrary dimensions. This is along the same lines as [1] where photon and graviton were classified. We do classification explicitly for gauge groups SO( N ) SU( all but our method easily generalizable to other Lie groups. The construction involves combining not-necessarily-permutation-symmetric of photons those adjoint scalars into permutation symmetric S-matrix. list both components construction, i.e well non-symmetric four point S-matrices, dimensions . Lagrangians that generate D ? 9 present relevant counting lower Local can be written down following method. also express Yang-Mills S-matrix with exchange terms basis structures.