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arXiv · 1909.10352

Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints

Luca Cassia·Rebecca Lodin·Aleksandr Popolitov·Maxim Zabzine
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Abstract

Using the ideas from the BPS/CFT correspondence, we give an explicit recursive formula for computing supersymmetric Wilson loop averages in 3d $\mathcal{N}=2$ Yang-Mills-Chern-Simons $U(N)$ theory on the squashed sphere $S^3_b$ with one adjoint chiral and two antichiral fundamental multiplets, for specific values of Chern-Simons level $\kappa_2$ and Fayet-Illiopoulos parameter $\kappa_1$. For these values of $\kappa_1$ and $\kappa_2$ the north and south pole turn out to be completely independent, and therefore Wilson loop averages factorize into answers for the two constituent $D^2 \times S^1$ theories. In particular, our formula provides results for the theory on the round sphere when the squashing is removed.

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Luca Cassia, Rebecca Lodin, Aleksandr Popolitov, Maxim Zabzine. 2019-09-23. Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints. https://doi.org/10.1007/jhep12(2019)121

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