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Main Author: Elliot, Grant
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.00735
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_version_ 1866917792690733056
author Elliot, Grant
author_facet Elliot, Grant
contents In arXiv:1811.01577 the VOAs associated to 4d $\mathcal{N}=2$ class-S theories were constructed in addition to a generalization for non-simply laced Lie algebras. However, 6d (2,0) theories have an ADE classification, and therefore class-S theories which are engineered by them come in ADE types. Thus, these non-simply laced VOAs are not thought to correspond to 4d physical theories. Regardless, we analyze these VOAs and their Drinfeld-Sokolov reductions in an effort to determine their properties. We find that many of these reduced VOAs appear to correspond to actual 4d $\mathcal{N}=2$ SCFTs. Additionally, we find what appear to be $F_4$ instanton VOAs, and hence from the proposal of arXiv:2201.13435 these correspond to 3d $\mathcal{N}=4$ quiver gauge theories whose Coulomb branches are $F_4$ instanton moduli spaces. Using a construction of twisted class-S VOAs from non-simply laced ones, we find additional evidence that the $F_4$ instanton VOAs do not correspond to four-dimensional field theories and outline an analogous argument for the $G_2$ instanton case. Our method appears to be quite general and may be a promising technique for ruling out 4d origins of VOAs that are similar to those of 4d $\mathcal{N}=2$ SCFTs, in addition to constructing VOAs of actual 4d theories.
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spellingShingle Non-Simply Laced Class-S Vertex Operator Algebras
Elliot, Grant
High Energy Physics - Theory
In arXiv:1811.01577 the VOAs associated to 4d $\mathcal{N}=2$ class-S theories were constructed in addition to a generalization for non-simply laced Lie algebras. However, 6d (2,0) theories have an ADE classification, and therefore class-S theories which are engineered by them come in ADE types. Thus, these non-simply laced VOAs are not thought to correspond to 4d physical theories. Regardless, we analyze these VOAs and their Drinfeld-Sokolov reductions in an effort to determine their properties. We find that many of these reduced VOAs appear to correspond to actual 4d $\mathcal{N}=2$ SCFTs. Additionally, we find what appear to be $F_4$ instanton VOAs, and hence from the proposal of arXiv:2201.13435 these correspond to 3d $\mathcal{N}=4$ quiver gauge theories whose Coulomb branches are $F_4$ instanton moduli spaces. Using a construction of twisted class-S VOAs from non-simply laced ones, we find additional evidence that the $F_4$ instanton VOAs do not correspond to four-dimensional field theories and outline an analogous argument for the $G_2$ instanton case. Our method appears to be quite general and may be a promising technique for ruling out 4d origins of VOAs that are similar to those of 4d $\mathcal{N}=2$ SCFTs, in addition to constructing VOAs of actual 4d theories.
title Non-Simply Laced Class-S Vertex Operator Algebras
topic High Energy Physics - Theory
url https://arxiv.org/abs/2410.00735