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arXiv · 2112.03775

The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories

Andrew Neitzke·Fei Yan
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Abstract

We consider the quantum UV-IR map for line defects in class $S$ theories of $\mathfrak{gl}(3)$-type. This map computes the protected spin character which counts framed BPS states with spin for the bulk-defect system. We give a geometric method of computing this map motivated by the physics of five-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills theory, and compute it explicitly in various examples. As a spin-off we propose a new way of computing a certain specialization of the HOMFLY polynomial for links in $\mathbb{R}^3$, as a sum over BPS webs attached to the link.

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Andrew Neitzke, Fei Yan. 2021-12-07. The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories. https://doi.org/10.1007/jhep09(2022)081

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