A new twist on dS/CFT

TL;DR

The authors argue that dS/CFT should be formulated with unitary principal series representations rather than highest-weight modules, a choice that clashes with finite de Sitter entropy. They resolve this by introducing a q-deformation of the isometry group at roots of unity in the 2D case, yielding finite-dimensional unitary representations that smoothly limit to the principal series in the classical limit. A concrete construction in dS2 shows how these cyclic representations can support a qdS/CFT duality with a finite entropy, addressing key entropy-compatibility issues and offering a path toward a microscopic holographic description of de Sitter space. The work outlines a broader program involving higher dimensions and interacting q-CFTs, and discusses how the framework interacts with existing concerns about 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.