Remarks on Associated Varieties and Minimal Tension Holography
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911062065938432 |
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| author | Ferrari, Andrea E. V. |
| author_facet | Ferrari, Andrea E. V. |
| contents | We comment on certain analogies that have recently emerged between path integral localisation phenomena in minimal tension string theory on $\mathrm{AdS}_3\times S^3\times T^4$ and associated varieties of boundary vertex algebras of 3d $\mathcal{N}=4$ theories. We give evidence for the fact that the path integral localisation relies on an intriguing relation between the conformal boundary of $\mathrm{AdS}_3$ and the associated variety of $V_1(\mathfrak{psl}(2|2))$, (the complexification of) the affine algebra that enters the world-sheet description of the string theory. We explain the origin of certain operators (related to ``secret representations") that have appeared in this description. Based on the expectation that similar statements will hold for $\mathrm{AdS}_5\times S^5$, we explicitly write down free field realisations of $V_1(\mathfrak{psl}(4|4))$ that may hopefully be useful to study the world-sheet dual of free $\mathcal{N}=4$ SYM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on Associated Varieties and Minimal Tension Holography Ferrari, Andrea E. V. High Energy Physics - Theory Quantum Algebra We comment on certain analogies that have recently emerged between path integral localisation phenomena in minimal tension string theory on $\mathrm{AdS}_3\times S^3\times T^4$ and associated varieties of boundary vertex algebras of 3d $\mathcal{N}=4$ theories. We give evidence for the fact that the path integral localisation relies on an intriguing relation between the conformal boundary of $\mathrm{AdS}_3$ and the associated variety of $V_1(\mathfrak{psl}(2|2))$, (the complexification of) the affine algebra that enters the world-sheet description of the string theory. We explain the origin of certain operators (related to ``secret representations") that have appeared in this description. Based on the expectation that similar statements will hold for $\mathrm{AdS}_5\times S^5$, we explicitly write down free field realisations of $V_1(\mathfrak{psl}(4|4))$ that may hopefully be useful to study the world-sheet dual of free $\mathcal{N}=4$ SYM. |
| title | Remarks on Associated Varieties and Minimal Tension Holography |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2507.13223 |