Supersymmetric vortex loops in 3D gauge theories

Abstract

We give a precise definition of BPS vortex loops in 3D non-abelian gauge theories with $\mathcal{N}=2$ SUSY by the path integral over fields with a prescribed singular behavior. We compute the expectation value of a BPS vortex loop on an ellipsoid. Using the result we revisit the known equivalence between Wilson and vortex loops in pure Chern-Simons theory. Naive computations of expectation values in $\mathcal{N}=2$ theory leads to an unwanted shift of parameters in the rule of correspondence. We resolve the problem by relating the shift to the global anomaly of $\mathcal{N}=2$ SUSY quantum mechanics. For theories with $U(N)$ gauge group we also develop an alternative description of vortex loops in terms of 1D $\mathcal{N}=2$ SUSY quantum mechanics on their worldline. For vortex loops in $\mathcal{N}=4$ theories, our construction reproduces some of the quiver GLSMs of Assel and Gomis.

58 pages; v2: a section added in the appendix, version to appear in JHEP

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Seiberg Duality in Chern-Simons Theory
• Witten Index and Wall Crossing
• Gauge Theory, Ramification, And The Geometric Langlands Program
• GLSM's for partial flag manifolds
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
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Cited by in corpus (4)

• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Abelian dualities and line defect indices for 3d gauge theories
• Lattice defect networks in 2d Yang-Mills