Witten's conformal boundary condition admits no half-supersymmetric extension in linearized minimal supergravity because supersymmetry maps the natural gravitino datum to the trace-free extrinsic curvature left unfixed by the conformal prescription.
Role of conformal three geometry in the dynamics of gravitation
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α' corrections leave the metric of self-dual instantons unmodified but correct the dilaton and axion fields via Gauss-Bonnet and Pontrjagin terms, with no net correction to the Euclidean action to first order.
One-loop metric fluctuations produce secularly growing IR divergences in the Hartle-Hawking wavefunction for complex saddles on R x S3, identical in leading order to the Lorentzian de Sitter case after UV renormalization.
Boundary conditions in GR for axially symmetric rotating dust can reproduce effects usually attributed to dark matter.
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IR behaviour of one-loop complex $\mathbb{R}\times S^3$ saddles
One-loop metric fluctuations produce secularly growing IR divergences in the Hartle-Hawking wavefunction for complex saddles on R x S3, identical in leading order to the Lorentzian de Sitter case after UV renormalization.