Superconformal Indices of 3d $\mathcal{N}=2$ SCFTs and Holography
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| Format: | Preprint |
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2024
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| author | Bobev, Nikolay Choi, Sunjin Hong, Junho Reys, Valentin |
| author_facet | Bobev, Nikolay Choi, Sunjin Hong, Junho Reys, Valentin |
| contents | We study the superconformal index of 3d $\mathcal{N}=2$ superconformal field theories on $S^1\times_ω S^2$ in the Cardy-like limit where the radius of the $S^1$ is much smaller than that of the $S^2$. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d $\mathcal{N}=2$ holographic superconformal field theories describing the low-energy dynamics of $N$ M2-branes and derive closed form expressions, valid to all orders in the $1/N$ expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS$_4$ and the four-derivative corrections to 4d gauged supergravity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superconformal Indices of 3d $\mathcal{N}=2$ SCFTs and Holography Bobev, Nikolay Choi, Sunjin Hong, Junho Reys, Valentin High Energy Physics - Theory We study the superconformal index of 3d $\mathcal{N}=2$ superconformal field theories on $S^1\times_ω S^2$ in the Cardy-like limit where the radius of the $S^1$ is much smaller than that of the $S^2$. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d $\mathcal{N}=2$ holographic superconformal field theories describing the low-energy dynamics of $N$ M2-branes and derive closed form expressions, valid to all orders in the $1/N$ expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS$_4$ and the four-derivative corrections to 4d gauged supergravity. |
| title | Superconformal Indices of 3d $\mathcal{N}=2$ SCFTs and Holography |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.13177 |