In AdS the fully gravitational Hartle-Hawking wave function acquires a nontrivial one-loop phase while the partially frozen version stays real and positive; a partially frozen de Sitter sphere shows phase cancellation.
AdS one-loop partition functions from bulk and edge characters
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Edge partition functions for totally symmetric tensors in dS_{d+1} are decomposed under so(d), with the linearized gravity case receiving contributions from shift-symmetric fields on S^{d-1} suggesting an embedded brane interpretation.
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A Tale of Two Hartle-Hawking Wave Functions: Fully Gravitational vs Partially Frozen
In AdS the fully gravitational Hartle-Hawking wave function acquires a nontrivial one-loop phase while the partially frozen version stays real and positive; a partially frozen de Sitter sphere shows phase cancellation.
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De Sitter Horizon Edge Partition Functions
Edge partition functions for totally symmetric tensors in dS_{d+1} are decomposed under so(d), with the linearized gravity case receiving contributions from shift-symmetric fields on S^{d-1} suggesting an embedded brane interpretation.