Scattering amplitudes in N=4 super Yang-Mills theory were studied
extensively in recent years, and the high amount of symmetry in the
theory led to the discovery of many relations among them. In
particular, dual superconformal symmetry has been established for
planar tree-level amplitudes. Dual and standard superconformal
symmetry together constitute Yangian symmetry, which is a distinct
sign of the integrable structure in the planar theory.
In analogy to the action of the symmetries on local gauge invariant
operators, possible deformations of the free symmetry generators can
be studied. At tree level, this reveals that a particular deformation
restores superconformal symmetry at singularities which occur when two
external momenta become collinear. The deformated generators still see
"spurious" singularities of naive invariants and thus symmetry alone
appears to uniquely determine all tree-level amplitudes.
Focusing on the aforementioned deformations, I will give an
introduction to the recent developments and current status.