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Register a new userIntegrability of Smooth Wilson Loops in N=4 Superspace
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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.
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We study dual conformal transformations of minimal area surfaces in $AdS_5 times S^5$ corresponding to holographic smooth Wilson loops and some other related observables. To act with dual conformal transformations we map the string solutions to the dual space by means of T-duality, then we apply a conformal transformation and finally T-dualize back to the original space. The transformation maps between string solutions with different boundary contours. The boundary contours of the minimal surfaces are not mapped back to the AdS boundary, and the regularized area of the surface changes.
We construct new families of 1/4 BPS Wilson loops in circular quiver $mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops. The new operators are cohomologically equivalent to bosonic 1/4 BPS Wilson loops and are then amenable of exact evaluation via localization techniques. Moreover, in the case of orbifold ABJM theory we identify the corresponding gravity duals for some of the 1/4 and 1/2 BPS Wilson loops.
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In a {cal N}=1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in {cal N}=4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/epsilon^2 pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g^2. We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results.
We find a general formula for the operator mixing on the $mathbb{S}^4$ of chiral primary operators (CPO) for the ${cal N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general ${cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${cal N}=4$ theory.
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