Dual conformal symmetry on the light-cone

Understand

We study the properties of conformal operators in the SL(2) sector of planar N=4 SYM and its supersymmetric SL(2|2) extension.

• The correlation functions of these operators and their form factors with respect to asymptotic on-shell states are determined in the appropriate limit by two different polynomials which can be identified as eigenstates of the dilatation operator in the coordinate and momentum representations, respectively.
• We argue that, in virtue of integrability of the dilatation operator, the two polynomials satisfy a duality relation -- they are proportional to each other upon an appropriate identification of momenta and coordinates.
• Combined with the conventional N=4 superconformal symmetry, this leads to the dual superconformal symmetry of the dilatation operator.