Supersymmetric vortex loops in 3D gauge theories

Abstract

Abstract We give a precise definition of BPS vortex loops in 3D non-abelian gauge theories with $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 SUSY quantum mechanics on their worldline. For vortex loops in $$ \mathcal{N} $$ N = 4 theories, our construction reproduces some of the quiver GLSMs of Assel and Gomis.