Abstract
We present new circular Wilson loops in three-dimensional mathcal{N} = 4 quiver Chern-Simons-matter theory on S3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.
Highlights
We present new circular Wilson loops in three-dimensional N = 4 quiver Chern-Simons-matter theory on S3
We aim to study here circular Wilson loops in three-dimensional N = 4 theories that are continuously connected by marginal deformations to the usual 1/4 BPS Gaiotto-Yin (“bosonic”) Wilson loop [15]
This paper reorganized the space of known Wilson loop operators in N = 4 Chern-Simonsmatter theories in three dimensions, which we call hyperloops, and generalized it considerably to include loops preserving 1, 2, 4 and 8 supercharges
Summary
We define moment maps and currents, which are bilinears of the hypermultiplets and twisted hypermultiplets in the adjoint representation of U(NI ), as follows μI a b. For the I + 1 node one can define νI+1 = qIaqIa. For example, for the I + 1 node one can define νI+1 = qIaqIa Note that in this notation the index of the moment maps represents the node under which they are charged, rather than the fields they are made of, as is the case in the notation of [1, 12]. The moment maps can be thought of as the generalization to N = 4 of the N = 2 scalar σ, though the latter is an auxiliary field in an off-shell formulation while we work in an on-shell formulation.
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