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arXiv · 2212.03133

Current Algebra Levels in the $E_8$ Theory

Jacques Distler·Grant Elliot
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Abstract

The class-S theories of type $E_8$ were analyzed in \cite{Chacaltana:2018vhp}. The basic building blocks consisted of 49,836 isolated SCFTs (three-punctured spheres). In 244 cases, there were undetermined levels for the flavour symmetry current algebra. Here, we rectify that omission. Using S-duality and nilpotent Higgsing we compute the levels of 235 of the 244. There remain 9 three-punctured spheres with unknown levels. Along the way, we provide a detailed discussion of the Drinfeld-Sokolov reduction of the VOA, which captures various features of the Higgs branch RG flows arising from giving a VEV to a nilpotent moment map.

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Jacques Distler, Grant Elliot. 2022-12-06. Current Algebra Levels in the $E_8$ Theory. https://arxiv.org/abs/2212.03133

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