Supersymmetric vortex loops in 3D gauge theories. (English) Zbl 1522.81630
Summary: 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 \(\mathrm{U}(N)\) 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.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T45 | Topological field theories in quantum mechanics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Keywords:
Chern-Simons theories; field theories in lower dimensions; supersymmetric gauge theory; Wilson loop; ’t Hooft and Polyakov loopsReferences:
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