1/3 BPS loops and defect CFTs in ABJM theory

We address a longstanding question of whether ABJM theory has Wilson loop operators preserving eight supercharges (so 1/3 BPS). We present such Wilson loops made of a large supermatrix combining two 1/2 BPS Wilson loops. We study the spectrum of operator insertions into them including the displacement operator and several others and study their correlation functions. Another natural construction arising in this context are Wilson loops with alternating superconnections. This amounts to including "defect changing operators" along the loop, similar to a discrete cusp. This insertion is topological and preserves two supercharges. We study the multiplet of this operator and how it can be used to introduce further operators. We also construct the defect conformal manifold arising from marginal defect operators.