IAS Quantum Aspects of Black Holes Group Meeting

Abstract: I will discuss the Euclidean path integral of minimal higher spin theory on the four-sphere and argue for a gluing formula in which the four-sphere is obtained by joining two hemispheres along an $S^3$ boundary. The resulting boundary theory is the $Sp(N)$-invariant sector of $N$ anticommuting, conformally coupled scalars, with conformal higher spin gauge fields mediating the gluing. This $S^3$ theory was previously shown to compute the Hartle–Hawking wavefunction in dS$_4$/CFT$_3$ at future infinity, whereas here we realize it with conformal boundary conditions at finite size, and the four-sphere partition function captures aspects of its norm. By supersymmetrising the gluing formula we obtain a $\mathcal{N}=2$ SCFT as the boundary theory, while the leading piece of the four-sphere partition function is $2^N$.