Abstract
We study a family of circular BPS Wilson loops in N=6 super Chern-Simons-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 framing dependence 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.
Highlights
Exact functions which interpolate from weak to strong coupling
We study a family of circular BPS Wilson loops in N = 6 super ChernSimons-matter theories, generalizing the usual 1/2-BPS circle
Supersymmetric Wilson loops in U(N )×U(M ) ABJ(M) theory can be constructed [23] as the holonomy of a generalized gauge connection
Summary
Apart from the case of the equatorial circle [26] nothing is known about the quantum properties of this class of Wilson loops We start their investigation by considering the simplest (but non-trivial) generalization of the equator, namely the latitude on S2 xμ = (sin θ0, cos θ0 cos τ, cos θ0 sin τ ) with π π. In this case the general form (2.3) and (2.2) of the couplings is greatly simplified. The usual 1/2-BPS circle is recovered by setting α π 4 and θ0 For this choice of the parameters the last two equations in (2.12) and (2.13) are identically satisfied and the supersymmetry is enhanced from 1/6 to 1/2
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