We construct a generalized cusped Wilson loop operator in N = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S 2 by a conformal transformation, realize a threedimensional analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U (N ) × U (M ) gauge group and its expectation value is expressed as the holonomy of a suitable super-connection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.arXiv:1208.5766v3 [hep-th]

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.

We analyse the phase structure of an N " 2 massive deformation of N " 4 SYM theory on an four-dimensional ellipsoid using recent results on supersymmetric localisation. Besides the 't Hooft coupling λ, the relevant parameters appearing in the theory and discriminating between the different phases are the hypermultiplet mass M and the deformation (or squashing) parameter Q. The master field approximation of the matrix model associated to the analytically continued theory in the regime Q " 2M and on the compact space, is exactly solvable and does not display any phase transition, similarly to N " 2 SU pN q SYM with 2N massive hypermultiplets. In the strong coupling limit, equivalent in our settings to the decompactification of the four-dimensional ellipsoid, we find evidence that the theory undergoes an infinite number of phase transitions starting at finite coupling and accumulating at λ " 8. Quite interestingly, the threshold points at which transitions occur can be pushed towards the weak coupling region by letting Q approach 2M .