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

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.

Mathematica and Python code included as auxiliary files, 55 pages, 51 figures

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• Holographic Wilson Loops
• The g-theorem and quantum information theory
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• Loop operators and S-duality from curves on Riemann surfaces
• Ω-deformation and quantization
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• Surface Defect, Anomalies and $b$-Extremization
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