Algebraic ER=EPR

 A paper I have been looking forward to with a lot of excitement since Netta's Strings talk has finally been arXived. It was worked on in conjunction with Hong Liu, who previously worked on algebra in AdS/CFT with Samuel Leutheusser in their subregion-subalgebra and emergent times papers. I had written a bit on algebraic ER=EPR in my notes on bulk reconstruction and subregion duality, where I briefly discussed this based on her Strings talk slides. 

[2311.04281] Algebraic ER=EPR and Complexity Transfer

Interestingly, the way I had tried to make an algebraic formulation of a ``strong" No Transmission Principle had a lot to do with the identification of type I and type III algebras. I may not arXiv that draft, but for the sake of it I may archive them here soon. For instance, in the paper by Engelhardt and Liu, the type I statement is that taking the bulk Hilbert space $\mathcal{H}_{bulk}=\mathcal{H}^{Fock}_{R}\otimes \mathcal{H}^{Fock}_{L}$, the boundary algebras $\mathcal{A}_{R}$ and $\mathcal{A}_{L}$ are type I if they are disconnected -- if they are connected, it must be type III (classically connected, or type II if quantum connected). The idea I had was that of a strong NTP, so that if the algebras are type I the bulk duals must be ``independent". The statement of the strong NTP was meant to be a strengthened version of NTP, saying that if the boundary CFTs are type I, they are disconnected and the bulk duals being disconnected should imply that the Cauchy slices are incomplete. I was yet to make this more precise when I saw Engelhardt's Strings talk.