Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
Higuchi,Quantum linearization instabilities of de Sitter space-time
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Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.
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dS$^4$ Metamorphosis
Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
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Gravitational Hilbert spaces: invariant and co-invariant states, inner products, gauge-fixing, and BRST
Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.