Stability in gauged extended supergravity
Extended supergravity theories with gauged SO(N) internal symmetry have, for \(N\geq 4\), 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 a 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.
scientific article; zbMATH DE number 3979970
scientific article