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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.00735 |
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| _version_ | 1866917792690733056 |
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| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| 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 |