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.
Boundary conditions in supergravity on a manifold with boundary
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abstract
We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary (``downstairs'') and orbifold (``upstairs'') pictures, we present a bulk-plus-boundary/brane action for the five-dimensional (on-shell) supergravity which is supersymmetric with the use of fewer boundary conditions than were previously employed. The required Gibbons-Hawking-like Y-term and many other aspects of the boundary/orbifold picture correspondence are discussed.
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A Linearized Obstruction to the Supersymmetric Extension of Conformal Boundary Conditions in Euclidean Gravity
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.