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.

arXiv comment58 pages; v2: a section added in the appendix, version to appear in JHEP

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