Notes on hyperloops in N $$ \mathcal{N} $$ = 4 Chern-Simons-matter theories

Abstract

Abstract We present new circular Wilson loops in three-dimensional N $$ \mathcal{N} $$ = 4 quiver Chern-Simons-matter theory on S 3. 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.

Keywords

• Chern-Simons Theories
• Supersymmetric Gauge Theory
• Wilson, ‘t Hooft and Polyakov loops