A new twist on dS/CFT

TL;DR

This paper proposes a q-deformed quantum group approach to the dS/CFT correspondence, replacing classical isometry groups with finite-dimensional representations to better account for de Sitter entropy.

Contribution

It introduces a q-deformation of the de Sitter isometry group, transforming infinite-dimensional principal series into finite-dimensional unitary representations, offering a potential microscopic explanation for de Sitter entropy.

Findings

Unitary principal series representations deform to finite-dimensional quantum group representations.

The q-deformation approach provides a promising framework for de Sitter entropy.

Detailed analysis performed for two-dimensional de Sitter space.

Abstract

We stress that the dS/CFT correspondence should be formulated using unitary principal series representations of the de Sitter isometry group/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 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.