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Constraints are not enough
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Constraints are not enough
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The Euclidean Einstein-Hilbert action is well-known to be unbounded below and thus to raise many questions regarding the definition of the gravitational path integral. A variety of works since the late 1980's have suggested that this problem disappears when one fixes a foliation of the spacetime and imposes the corresponding gravitational constraints. However, we show here that this approach fails with various classes of boundary conditions imposed on the foliation: compact slices without boundary, asymptotically flat, or asymptotically locally anti-de Sitter slices. We also discuss the idea of fixing the scalar curvature and Wick-rotating the conformal factor, and show that it also fails to produce an action bounded from below.
Forward citations
Cited by 4 Pith papers
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Spectral Admissibility of Real Observers in Euclidean de Sitter Gravity
The paper introduces a form-domain criterion and proves a sufficiency theorem that identifies which gapped observer sectors remain semiclassically admissible in Euclidean de Sitter gravity on the sphere.
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Horizon Edge Partition Functions in $\Lambda>0$ Quantum Gravity
Horizon edge mode spectra in de Sitter and Nariai spacetimes exhibit universal shift symmetries that produce novel symmetry breaking in one-loop partition functions.
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How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
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When do real observers resolve de Sitter's imaginary problem?
Real observers remove the de Sitter imaginary phase only if their fluctuations share the conformal factor's negative modes; metric-independent sectors factorize and preserve the phase.
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