We show that the form of the recently proposed subleading soft graviton and gluon theorems in any dimension are severely constrained by elementary arguments based on Poincaré and gauge invariance as well as a self-consistency condition arising from the distributional nature of scattering amplitudes. Combined with the assumption of a local form as it would arise from a Ward identity the orbital part of the subleading operators is completely fixed by the leading universal Weinberg soft pole behavior. The polarization part of the differential subleading soft operators in turn is determined up to a single numerical factor for each hard leg at every order in the soft momentum expansion. In four dimensions, factorization of the Lorentz group allows to fix the subleading operators completely.

We translate between different formulations of Yangian invariants relevant for the computation of tree-level scattering amplitudes in N=4 super-Yang--Mills theory. While the R-operator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally well be connected to the permutations encoded by on-shell graphs.Comment: 44 pages; replaced with published versio

We investigate Yangian invariance of deformed on-shell diagrams with D = 4, N = 4 superconformal symmetry. We find that invariance implies a direct relationship between the deformation parameters and the permutation associated to the on-shell graph. We analyse the connection with deformations of scattering amplitudes in N = 4 super-Yang-Mills theory and the possibility of using the deformation parameters as a regulator preserving Yangian invariance. A study of higher-point tree and loop graphs suggests that manifest Yangian invariance of the amplitude requires trivial deformation parameters.

In this Letter, we establish Yangian symmetry of planar N=4 supersymmetric Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover, we propose an off-shell extension of our statement, which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to the integrable Aharony-Bergman-Jafferis-Maldacena theory but not to the nonintegrable N=1 supersymmetric Yang-Mills theory.