Dual conformal symmetry on the light-cone

TL;DR

This paper explores dual superconformal symmetry in the SL(2) sector of planar N=4 SYM, revealing how integrability and symmetry constraints determine the spectrum of the dilatation operator at one loop.

Contribution

It demonstrates that dual superconformal symmetry arises from integrability and can fix the dilatation operator's spectrum at lowest order in the coupling.

Findings

Dual superconformal symmetry is established for the dilatation operator.

The spectrum is fixed by symmetry at one-loop order.

The Baxter Q-operator generates the dual symmetry in the large spectral parameter limit.

Abstract

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. We demonstrate that this symmetry is powerful enough to fix the eigenspectrum of the dilatation operator to the lowest order in the coupling. We use the relation between the one-loop dilatation operator and Heisenberg spin chain to show that, to lowest order in the coupling, the dual symmetry is generated by the Baxter Q-operator in the limit of large spectral parameter.