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Current Algebra Levels in the $E_8$ Theory
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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.
Forward citations
Cited by 2 Pith papers
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On Twisted $A_{2n}$ Class-S Theories
A proposed formula and puncture data for twisted A2n Coulomb branch dimensions, built on a conjectured metaplectic special map d'.
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Even More On Twisted $A_{2n}$ Class-S Theories
An order-4 twist automorphism and local polynomial constraints determine the Coulomb branch Hitchin systems for twisted A_{2n} class-S punctures, with explicit Seiberg-Witten curves for examples.
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