Stability in gauged extended supergravity

Extended supergravity theories with gauged SO(N) internal symmetry have, for N> or =4, scalar field potentials which are unbounded below. Nevertheless, it is argued that the theories have ground states with anti-de Sitter background geometry which are stable against fluctuations which vanish sufficiently fast at spatial infinity. Stability is implied because the appropriate conserved energy functional is positive for such fluctuations. Anti-de Sitter space is not globally hyperbolic, but the boundary conditions required for positive energy are also shown to give free field theories with well-defined Cauchy problem. New information on the particle representations of OSp(1, 4) supersymmetry is presented as part of the argument. Supersymmetry requires boundary conditions for spin 0 fields such that only the improved stress tensor leads to a conserved energy functional. Although the stability arguments support the view that gauged supergravity theories are acceptable quantum field theories, the problem of a large cosmological term in the Ads phase of the theories is still unsolved