q-Deformed de Sitter/Conformal Field Theory Correspondence

TL;DR

This paper explores a q-deformed version of the dS/CFT correspondence, leading to finite-dimensional representations and a finite Hilbert space, and computes the entanglement entropy across the cosmological horizon in 3D de Sitter space.

Contribution

It generalizes the q-deformation approach to three-dimensional de Sitter space and calculates the entanglement entropy in this quantum-deformed setting.

Findings

Finite-dimensional cyclic unitary representations for 3D de Sitter

A formulation of dS/CFT with finite-dimensional Hilbert space

Computed entanglement entropy across the cosmological horizon

Abstract

Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown for the case of two-dimensional de Sitter, there was a natural q-deformation of the conformal group, with q a root of unity, where the unitary principal series representations become finite-dimensional cyclic unitary representations. Formulating a version of the dS/CFT correspondence using these representations can lead to a description with a finite-dimensional Hilbert space and unitary evolution. In the present work, we generalize to the case of quantum-deformed three-dimensional de Sitter spacetime and compute the entanglement entropy of a quantum field across the cosmological horizon.