New twist on the dS/CFT correspondence

We stress that the dS/CFT correspondence should be formulated using unitary principal series representations of the de Sitter isometry group or conformal group, rather than highest-weight representations as originally proposed. These representations, however, are infinite dimensional, and so do not account for the finite gravitational entropy of de Sitter space in a natural way. We then propose to replace the classical isometry group by a q-deformed version. This is carried out in detail for two-dimensional de Sitter space and we find that the unitary principal series representations deform to finite-dimensional unitary representations of the quantum group. We believe this provides a promising microscopic framework to account for the Bekenstein-Hawking entropy of de Sitter space.