Abstract
We study half-BPS line operators in 3d mathcal{N} = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called “Wilson lines” and “vortex lines,” and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulomb-branch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis.
Highlights
BPS line operators in supersymmetry gauge theories hold a wealth of algebraic and geometric structure
We study half-BPS line operators in 3d N = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions
We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data
Summary
BPS line operators in supersymmetry gauge theories hold a wealth of algebraic and geometric structure. A systematic study of half-BPS vortex lines in 3d N = 4 quiver gauge theories — both abelian and nonabelian — was initiated more recently by Assel and Gomis [54] using IIB brane constructions [55], akin to the constructions of surface operators in [31, 56]. Part of this paper will be devoted to first characterizing a large class of vortex lines in terms of algebraic data, and proposing a precise computational scheme (based on the algebraic data) to determine the spaces of local operators at junctions. We test this scheme in several nontrivial examples
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