Abstract
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A gauge-covariant action of the Yangian generators on the Wilson line is established that generalizes previous constructions built upon path variations. Employing these generators the Yangian symmetry is proven for general paths in non-chiral N=4 superspace at the first perturbative order. The bi-local piece of the level-one generators requires the use of a regulator due to divergences in the coincidence limit. We perform regularization by point splitting in detail, thereby constructing additional local and boundary contributions as regularization for all level-one Yangian generators. Moreover, the Yangian algebra at level one is checked and compatibility with local kappa-symmetry is established. Finally, the consistency of the Yangian symmetry is shown to depend on two properties: The vanishing of the dual Coxeter number of the underlying superconformal algebra and the existence of a novel superspace "G-identity" for the gauge field theory. This tightly constrains the conformal gauge theories to which integrability can possibly apply.
Highlights
The maximally supersymmetric gauge field theory in four dimensions [1, 2] — N = 4 super Yang-Mills (SYM) — with SU(N ) gauge group has become something like the drosophila of gauge field theories
Wilson loops with scalar coupling which are null in a ten-dimensional sense enjoy eight additional translational symmetries in superspace which is closely related to kappa-symmetry of string theory [13]
We have investigated the Yangian symmetry of Wilson loops in detail and proved the existence of this hidden symmetry at leading perturbative order
Summary
The maximally supersymmetric gauge field theory in four dimensions [1, 2] — N = 4 super Yang-Mills (SYM) — with SU(N ) gauge group has become something like the drosophila of gauge field theories This is due to its remarkable symmetry structure and the observed integrability [3] in the planar limit of the theory. According to the AdS/CFT correspondence [8] the N = 4 SYM model is dual to the type IIB superstring on an AdS5 × S5 space-time background Within this setting there is a natural Wilson loop for N = 4 SYM that extends the standard definition, where one integrates the gauge field Aμ along a closed path in R1,3. The presence of six real adjoint scalar fields in the theory allows for a coupling to an extended path Con R1,3 × S5, to wit [9, 10]
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