The Ghost Condensate in N=1 Supergravity

TL;DR

This work constructs a ghost condensate within N=1 supergravity using a general framework for locally supersymmetric higher-derivative chiral superfield actions. It demonstrates a ghost-condensate vacuum in de Sitter space, with a scalar sector free of ghosts and gradient instabilities, and a fermion sector comprising a massless chiral fermion and a massless gravitino; supersymmetry is spontaneously broken by the time-dependent scalar, with the chiral fermion acting as the Goldstone mode while the gravitino mass remains zero because the vacuum has W=0, avoiding the super-Higgs effect. Stabilization of scalar fluctuations is achieved by introducing additional higher-derivative SUSY terms, which shift the condensate and de Sitter scales but preserve the massless fermion and gravitino. The results yield a consistent ghost-condensate supergravity theory and motivate further exploration of supersymmetric Galileon extensions and string-theory embeddings.

Abstract

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.