dS$^4$ Metamorphosis
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911610304462848 |
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| author | Anninos, Dionysios Baracco, Chiara Letsios, Vasileios A. Mühlmann, Beatrix |
| author_facet | Anninos, Dionysios Baracco, Chiara Letsios, Vasileios A. Mühlmann, Beatrix |
| contents | We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the $S^3$ cut is the $\mathrm{Sp}(N)$ invariant sector of $N\in \mathbb{Z}^+$ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary $\mathrm{Sp}(N)$ theory was previously shown to compute the Hartle-Hawking wavefunction at $\mathcal{I}^+$ in the higher spin dS$_4$/CFT$_3$ correspondence. In contrast to the infinite spatial volume of $\mathcal{I}^+$, here the conformal fields populate a finite size $S^3$ hypersurface of $S^4$. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an $\mathcal{N}=2$ superconformal boundary field theory coupled to $U(N)$ invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is $2^N$, and we observe exact cancellations at one-loop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | dS$^4$ Metamorphosis Anninos, Dionysios Baracco, Chiara Letsios, Vasileios A. Mühlmann, Beatrix High Energy Physics - Theory General Relativity and Quantum Cosmology We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the $S^3$ cut is the $\mathrm{Sp}(N)$ invariant sector of $N\in \mathbb{Z}^+$ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary $\mathrm{Sp}(N)$ theory was previously shown to compute the Hartle-Hawking wavefunction at $\mathcal{I}^+$ in the higher spin dS$_4$/CFT$_3$ correspondence. In contrast to the infinite spatial volume of $\mathcal{I}^+$, here the conformal fields populate a finite size $S^3$ hypersurface of $S^4$. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an $\mathcal{N}=2$ superconformal boundary field theory coupled to $U(N)$ invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is $2^N$, and we observe exact cancellations at one-loop. |
| title | dS$^4$ Metamorphosis |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.19812 |