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

• Main Authors: Cassia, Luca, Lodin, Rebecca, Popolitov, Aleksandr, Zabzine, Maxim
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2019
• Subjects: High Energy Physics - Theory hep-th; Mathematical Physics math-ph; FOS Physical sciences; South Pole; South pole
• Online Access: https://dx.doi.org/10.48550/arxiv.1909.10352; https://arxiv.org/abs/1909.10352

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 $κ_2$ and Fayet-Illiopoulos parameter $κ_1$. For these values of $κ_1$ and $κ_2$ 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. : 30 pages, 1 figure; v2: typos fixed, JHEP version