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dS4 Metamorphosis
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DOI：10.1007/jhep07(2026)178.png)
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Abstract
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We study the Euclidean path integral of higher spin gravity on S4. Based on a one-loop analysis, we are led to a gluing formula expressing the S4 path integral in terms of an underlying S3 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 S3 cut is the Sp(N) invariant sector of N ∈ ℤ+ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary Sp(N) theory was previously shown to compute the Hartle-Hawking wavefunction at $$ {\mathcal{I}}^{+} $$ in the higher spin dS4/CFT3 correspondence. In contrast to the infinite spatial volume of $$ {\mathcal{I}}^{+} $$ , here the conformal fields populate a finite size S3 hypersurface of S4. 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 2N, and we observe exact cancellations at one-loop.
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