Dual conformal symmetry on the light-cone

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.

27 pages

References in corpus (13)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Baxter's Q-operators for supersymmetric spin chains
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• Descent equations for superamplitudes

Cited by in corpus (7)

• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Tailoring Non-Compact Spin Chains
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• On Soft Theorems And Form Factors In N=4 SYM Theory
• A new representation for two- and three-point correlators of operators from sl(2) sector
• Correlators with $s{\ell }_2$ Yangian symmetry
• Wilson Loop Form Factors: A New Duality