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 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.
Highlights
In this paper, we discuss the relation between dual superconformal symmetry in planar N = 4 SYM [1] and integrability of dilatation operator in the same theory.S.É
The very fact that such a relation exists in planar N = 4 SYM immediately leads to an enhancement of the symmetry – the conventional N = 4 superconformal symmetry of Wilson loops and correlation functions combined with the duality relation imply the dual superconformal symmetry of the scattering amplitudes
The correlation functions of these operators and their form factors with respect to asymptotic on-shell states are determined by two different polynomials which can be identified as eigenstates of the dilatation operator in the momentum and coordinate representations
Summary
The AdS/CFT correspondence suggests that, despite the fact that the scattering amplitudes and dilatation operator have different meaning in planar N = 4 SYM, they should have the same symmetries at strong coupling related to those of sigma-model on AdS5 × S5.
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