dS4 Metamorphosis

A bstract 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 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 $$ {\mathcal{I}}^{+} $$ I + in the higher spin dS 4 /CFT 3 correspondence. In contrast to the infinite spatial volume of $$ {\mathcal{I}}^{+} $$ 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 $$ \mathcal{N} $$ 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.