Comments on Entanglement Entropy in the dS/CFT Correspondence

TL;DR

This paper tackles defining holographic entanglement entropy in de Sitter space within the dS/CFT framework. It proposes that $S_A = \frac{\text{Area}_{\rm dS}}{4 G_N}$ is obtained by analytic continuation from extremal surfaces in Euclidean AdS via a double Wick rotation, allowing complex-valued surfaces in $dS$. The authors validate the approach by studying a toy $(Sp(N))$ CFT dual to Vasiliev's higher-spin theory, finding $S_A = -\frac{N V_{d-2}}{6(d-2)(4\pi)^{(d-2)/2}}\frac{1}{\varepsilon^{d-2}}$, i.e., the entropy is negative and the result aligns with the analytic continuation. These findings suggest intrinsic complex structure and sign differences in the dS/CFT entanglement entropy, with potential relevance to the $dS_4/CFT_3$ case and extensions to more general spacetimes such as Schwarzschild-$dS$.

Abstract

We consider the entanglement entropy in the dS/CFT correspondence.In Einstein gravity on de Sitter spacetime we propose the holographic entanglement entropy as the analytic continuation of the extremal surface in Euclidean anti-de Sitter spacetime.Even though dual conformal field theories for Einstein gravity on de Sitter spacetime have not been known yet,we analyzed the free $Sp(N)$ model dual to Vasiliev's higher spin gauge theory as a toy model.In this model we confirmed the behaviour similar to our holographic result from Einstein gravity.