Abstract
We investigate the supersymmetric Wilson loops in $d=3$ $\mathcal{N}=4$ super Chern-Simons-matter theory obtained from non-chiral orbifold of ABJM theory. We work in both Minkowski spacetime and Euclidean space, and we construct 1/4 and 1/2 BPS Wilson loops. We also provide a complete proof that the difference between 1/4 and 1/2 Wilson loops is $Q$-exact with $Q$ being some supercharge that is preserved by both the 1/4 and 1/2 Wilson loops. This plays an important role in applying the localization techniques to compute the vacuum expectation values of Wilson loops. We also study the M-theory dual of the 1/2 BPS circular Wilson loop.
Highlights
After the discovery of AdS5/CFT4 correspondence [1,2,3], people have been interested in the AdS4/CFT3 correspondence
In Minkowski spacetime we have 1/2 BPS Wilson loops along null infinite straight lines, and 1/4 and 1/2 BPS Wilson loops along timelike infinite straight lines
In Euclidean space we have 1/4 and 1/2 Wilson loops along infinite straight lines, as well as circular 1/4 and 1/2 Wilson loops
Summary
After the discovery of AdS5/CFT4 correspondence [1,2,3], people have been interested in the AdS4/CFT3 correspondence. The Wilson loops in this N = 4 theory in fundamental representation are dual to M2-branes in AdS4 × S7/(Zn × Znk) spacetime. We find that there exists such an M2-brane that preserves half of the supersymmetries of the M-theory in AdS4 × S7/(Zn × Znk) spacetime This indicates that there should be half-BPS Wilson loops in such N = 4 SCSM theory. The supercharges preserved by this probe membrane correspond to the solution of γ01♯ǫ = ǫ Since it is compatible with the projection condition in (2.32), we arrive at the conclusion that the probe M2-brane put at α = θ1 = 0 is half BPS compared to the supersymmetries of M-theory in AdS4 × S7/Γn,k spacetime.
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