The Ghost Condensate in N=1 Supergravity
  We present the theory of a supersymmetric ghost condensate coupled to N=1
supergravity. This is accomplished using a general formalism for constructing
locally supersymmetric higher-derivative chiral superfield actions. The theory
admits a ghost condensate vacuum in de Sitter spacetime. Expanded around this
vacuum, the scalar sector of the theory is shown to be ghost-free with no
spatial gradient instabilities. By direct calculation, the fermion sector is
found to consist of a massless chiral fermion and a massless gravitino. By
analyzing the supersymmetry transformations, we find that the chiral fermion
transforms inhomogeneously, indicating that the ghost condensate vacuum
spontaneously breaks local supersymmetry with this field as the Goldstone
fermion. Although potentially able to get a mass through the super-Higgs
effect, the vanishing superpotential in the ghost condensate theory renders the
gravitino massless. Thus local supersymmetry is broken without the super-Higgs
effect taking place. This is in agreement with, and gives an explanation for,
the direct calculation.
