[From my Twitter thread]: Maybe it is just time to reboot dS holography altogether. No more double Wick rotations, start from ground up and tell me what for the love of god the FLM corrections to entanglement entropy are. My *educated guess* is that static path is the description where we should start from. We get a similar Ryu-Takayanagi-like formula, for which we have to find semiclassical corrections. Leaving technicalities, we’ll assume there is an FLM-type formula. And here is where I note an interesting point. Pseudo-entropy formalism for EE in dS implies that the relevant quantities like the modular Hamiltonian are also pseudo-valued, and while there seem to exist ways to describe pseudo-relative entropy with $K=-\log \tau $ ($\tau $ is a transition matrix) and have a first law of entanglement, in static patch this doesn’t seem to be the case, so finding a JLMS formula becomes neater. Intuitively as well modular flows make sense, which is a good check mathematically. Subsequently subregion-duality would make sense. In retrospect, bulk reconstruction is a slightly unintuitive thing, and perhaps this should be addressed earlier. On the other hand, maybe a mathematical approach could be better suited, starting from operator algebras that Chandrasekharan, Penington, Longo and Witten did. Whether subregion-subalgebra in static patch dS follow on those lines is not entirely clear to me, but if it does follow a Liu-Leutheusser-type formulation with type II_1 algebras, that would go a long way in clearing what exactly dS holography means. One interesting thing here is that opposed to type II_\infty algebras in crossed product AdS/CFT one has a nicer vN algebraic setting, and it would be good to ask how the entropy of subspaces/subalgebras (I’m not sure how to know which in dS yet) corresponds to bulk wedges. Maybe some corresponding notion of entanglement wedges could be derived? Will update the thread with the next set of comments.
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