Abstract
Anti-de Sitter space is the natural ground state of the O( N) gauged supergravity theories. If the excited states approach anti-de Sitter space sufficiently fast at infinity that one can define asymptotic anti-de Sitter Killing vectors, then the gravitational radiation obeys a reflective boundary condition and one can define asymptotic supercovariant constant spinor fields. If the boundary conditions are invariant under the supersymmetry transformations generated by these spinor fields, then all the zero rest-mass fields obey reflective boundary conditions which require that the “magnetic” components of the Weyl tensor and the spin-one field strength fall off faster than the “electric” components. The pseudo-scalar fields fall off faster than the scalar fields. Infinity is sufficiently flat that one can define a global OSp(4| N) algebra.
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