BPS Wilson loops in $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories

TL;DR

This paper constructs and analyzes a broad class of BPS Wilson loops in $ $ superconformal Chern-Simons-matter theories, exploring their properties, duals, and quantum equivalences, with implications for gauge/string duality and defect CFTs.

Contribution

It introduces a new family of BPS Wilson loops, studies their properties, duals, and quantum cohomological equivalences, extending known results in ABJM and orbifold theories.

Findings

Most general BPS Wilson loop connections cannot be decomposed into double-node connections.

Certain parameter choices recover known 1/6 and 1/4 BPS Wilson loops.

Quantum cohomological equivalence between fermionic and bosonic loops is strongly supported.

Abstract

In $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in $\mathcal N = 4$ orbifold ABJM theory. In the particular case of $\mathcal N = 2$ orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.