A localising AdS$_3$ sigma model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918297400770560 |
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| author | Eberhardt, Lorenz Gaberdiel, Matthias R. |
| author_facet | Eberhardt, Lorenz Gaberdiel, Matthias R. |
| contents | We construct a CFT with $\mathfrak{sl}(2,\mathbb{R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{SL}(2,\mathbb{R})_{k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{\rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$, as well as the recently discussed example of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${\rm AdS}_3$ backgrounds (at $k=3$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A localising AdS$_3$ sigma model Eberhardt, Lorenz Gaberdiel, Matthias R. High Energy Physics - Theory We construct a CFT with $\mathfrak{sl}(2,\mathbb{R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{SL}(2,\mathbb{R})_{k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{\rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$, as well as the recently discussed example of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${\rm AdS}_3$ backgrounds (at $k=3$). |
| title | A localising AdS$_3$ sigma model |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.09226 |