de Sitter supersymmetry revisited

Abstract

We present the basic N = 1 superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full SO(4, 2) group of conformal symmetries, which includes the de Sitter isometry group SO(4, 1) as a subgroup. The theories are ghost-free and the anti-commutator ∑ [subscript α] {Q [subscript α] , Q [superscript α †]} is positive. SUSY Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has non-zero Hawking temperature. The N = 1 theories are classically invariant under the SU(2, 2|1) superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the N = 4 theory, which is presented in appendix B.