We present a large new family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory. For an arbitrary curve on the three dimensional sphere one can add certain scalar couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out many more special cases which were not known before and could provide further tests of the AdS/CFT correspondence.

We discuss 2d duality transformations in the classical AdS 5 × S 5 superstring and their effect on the integrable structure. T-duality along four directions in the Poincaré parametrization of AdS 5 maps the bosonic part of the superstring action into itself. On the bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2, 4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transformation of the bosonic components of the current with a transformation on the fermionic ones. At the level of the action, this symmetry can be seen by combining the bosonic duality transformation with a similar one applied to part of the fermionic superstring coordinates. As a result, the full superstring action is mapped into itself, albeit in a different κ-symmetry gauge. One implication is that the dual model has the same superconformal symmetry group as the original one, and this may be seen as a consequence of the integrability of the superstring. The invariance of the Lax connection under the duality implies a map on the full set of conserved charges that should interchange some of the Noether (local) charges with hidden (non-local) ones and vice versa.

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We compute the one-loop correction to partition function of AdS 5 × S 5 superstring that should be representing k-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on k-wound circle at the boundary is that of a cone of AdS 2 with deficit 2π(1 − k). We compute the determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results. * Also at Lebedev Institute, Moscow. tseytlin@imperial.ac.uk