Discrete Symmetries Excluded by Quantum Breaking
  In this note we show that the cosmological domain wall and the de Sitter
quantum breaking problems complement each other in theories with discrete
symmetries that are spontaneously broken at low energies. Either the symmetry
is exact and there is a domain wall problem, or it is approximate and there
exists an inconsistent de Sitter minimum. This leaves no room for many
extension of the Standard Model based on such discrete symmetries. We give some
examples that include NMSSM, spontaneous CP violation at the weak scale and
some versions of the Peccei-Quinn scenario with discrete symmetries.
