Pure de Sitter Supergravity

Abstract

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

22 pages, version to appear in PRD; v4: minor typos corrected; v5: correction of torsion lagrangian (2.2); v6: Minor error in Sec.4.3 corrected. This simplifies previous proof that any zero mode vanishes identically