We study a family of circular BPS Wilson loops in N = 6 super ChernSimons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in N = 4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.

We investigate the most general non(anti)commutative geometry in N = 1 four dimensional superspace, invariant under the classical (i.e. undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which however allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative ⋆-product. We also consider the case of N = 2 euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry.

We compute two-point functions of chiral operators TrΦ 3 in N = 4 SU (N ) supersymmetric Yang-Mills theory to the order g 4 in perturbation theory. We perform explicit calculations using N = 1 superspace techniques and find that perturbative corrections to the correlators vanish for all N . While at order g 2 the cancellations can be ascribed to the nonrenormalization theorem valid for correlators of operators in the same multiplet as the stress tensor, at order g 4 this argument no longer applies and the actual cancellation occurs in a highly nontrivial way. Our result is obtained in complete generality, without the need of additional conjectures or assumptions. It gives further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N .

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