De Sitter supergravity with positive cosmological constant and generalised Lie superalgebras

Abstract

The modified conjugation law for fermion fields is suggested providing Hermiticity of the de Sitter supergravity action with the positive cosmological constant lambda >0. It is shown however that the modified conjugation leads to an indefinite metric Hilbert space, i.e. although de Sitter supergravity exists, it possesses ghosts. The corresponding N=1 supersymmetric de Sitter algebra is constructed. It is found that this algebra is not an ordinary Lie superalgebra but belongs to the class of generalised (Z2*Z2-graded) Lie superalgebras.