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We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS5 supergravity results. To study this phenomenon at the two-loop level (order g4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions.

In the cases of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS5 supergravity results. To study this phenomenon at the two-loop level (order g4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions.In the cases of 1/2-BPS operators of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop corrections. However, for weight k>4 the degeneracy is still there at the two-loop level. This behavior suggests that for a given weight k the degeneracy will be removed if perturbative corrections of sufficiently high order are taken into account. These results are in accord with the AdS/CFT duality conjecture. [Copyright &y& Elsevier]

We study a class of non-protected local composite operators which occur in the R-symmetry singlet channel of the OPE of two stress-tensor multiplets in N=4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an N=1 setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states. [Copyright &y& Elsevier]

We generalize the geometrical formulation of Wilson loops recently introduced in [1] to the description of Wilson Surfaces. For N = (2, 0) theory in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces with non-trivial coupling to scalars, together with their manifestly supersymmetric version. We derive explicit conditions which allow to classify these operators in terms of the number of preserved supercharges. We also discuss kappa-symmetry and prove that BPS conditions in six dimensions arise from kappa-symmetry invariance in eleven dimensions. Finally, we discuss super-Wilson Surfaces — and higher dimensional operators — as objects charged under global p-form (super)symmetries generated by tensorial supercurrents. To this end, the construction of conserved supercurrents in supermanifolds and of the corresponding conserved charges is developed in details. [ABSTRACT FROM AUTHOR]

We study supersymmetric Wilson loops from a geometrical perspective. To this end, we propose a new formulation of these operators in terms of an integral form associated to the immersion of the loop into a supermanifold. This approach provides a unifying description of Wilson loops preserving different sets of supercharges, and clarifies the flow between them. Moreover, it allows to exploit the powerful techniques of super- differential calculus for investigating their symmetries. As remarkable examples, we discuss supersymmetry and kappa-symmetry invariance. [ABSTRACT FROM AUTHOR]

Within the 풩 = 2 superspace perturbative formulation of ABJM theory, we derive the set of scalar Feynman integrals describing the four-point scattering amplitude of chiral matter fields. Using dimensional regularization (D = 3 - 2ϵ), we evaluate the integrals on-shell and we compare the result with that of a Wilson-loop computed in a light-like tetragon contour: we find matching results between both calculations after identifying the kinematical invariants. We discuss further implications and open questions. This work is a contribution to the proceedings of the 'XVIIth European Workshop on String Theory 2011' held in Padua, Italy, on September 2011. [ABSTRACT FROM AUTHOR]