LAUSR

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