Subleading analysis for $S^3$ partition functions of $\mathcal{N}=2$ holographic SCFTs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916382548951040 |
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| author | Geukens, Seppe Hong, Junho |
| author_facet | Geukens, Seppe Hong, Junho |
| contents | We investigate the 3-sphere partition functions of various 3d $\mathcal{N}=2$ holographic SCFTs arising from the $N$ stack of M2-branes in the 't Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy $F=-\log Z$ at the planar level, tracking the first subleading corrections in the large 't Hooft coupling $λ$ expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large $λ$ expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these $S^3$ partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS$_4$ backgrounds with the corresponding internal manifolds through holographic duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subleading analysis for $S^3$ partition functions of $\mathcal{N}=2$ holographic SCFTs Geukens, Seppe Hong, Junho High Energy Physics - Theory We investigate the 3-sphere partition functions of various 3d $\mathcal{N}=2$ holographic SCFTs arising from the $N$ stack of M2-branes in the 't Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy $F=-\log Z$ at the planar level, tracking the first subleading corrections in the large 't Hooft coupling $λ$ expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large $λ$ expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these $S^3$ partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS$_4$ backgrounds with the corresponding internal manifolds through holographic duality. |
| title | Subleading analysis for $S^3$ partition functions of $\mathcal{N}=2$ holographic SCFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.00845 |