The Ghost Condensate in N=1 Supergravity

TL;DR

This paper develops a supergravity theory with a ghost condensate, demonstrating a stable vacuum that spontaneously breaks local supersymmetry without generating a gravitino mass, providing new insights into supersymmetric ghost condensates.

Contribution

It introduces a formalism for constructing locally supersymmetric higher-derivative actions with ghost condensates, revealing spontaneous supersymmetry breaking without super-Higgs effect in supergravity.

Findings

The theory admits a ghost condensate vacuum in de Sitter space.

The scalar sector is ghost-free with no spatial instabilities.

The fermion sector includes a massless chiral fermion and gravitino, with supersymmetry spontaneously broken.

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.