Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory

In addition to the superconformal symmetry of the underlying Lagrangian, the scattering amplitudes in planar N=4 super-Yang-Mills theory exhibit a new, dual superconformal symmetry. We address the question of how powerful these symmetries are to completely determine the scattering amplitudes. We use the example of the NMHV superamplitudes to show that the combined action of conventional and dual superconformal symmetries is not sufficient to fix all the freedom in the tree-level amplitudes. We argue that the additional information needed comes from the study of the analytic properties of the amplitudes. The requirement of absence of spurious singularities, together with the correct multi-particle singular behavior, determines the unique linear combination of superinvariants corresponding to the n-particle NMHV superamplitude. The same result can be obtained recursively, by relating the n- and (n-1)-particle amplitudes in the singular collinear limit. We also formulate constraints on the loop corrections to the superamplitudes, following from the analytic behavior in the above limits. We then show that the holomorphic anomaly of the tree amplitudes leads to the breakdown of dual Poincare supersymmetry (which is equivalent to ordinary special conformal supersymmetry) of the ratio of the NMHV and MHV superamplitudes at one-loop level, but this anomaly does not affect dual conformal symmetry.