Abstract
According to the Ryu-Takayanagi prescription, the entanglement entropy of subsystems in the boundary conformal field theory (CFT) is proportional to the area of extremal surfaces in bulk asymptotically Anti-de Sitter (AdS) spacetimes. The flat-space limit of these surfaces is not well defined in the generic case. We introduce a new curve in the three-dimensional asymptotically AdS spacetimes with a well-defined flat-space limit. We find this curve by using a new vector, which is vanishing on it and is normal to the bulk modular flow of the original interval in the two-dimensional CFT. The flat-space limit of this new vector is well defined and gives rise to the bulk modular flow of the corresponding asymptotically flat spacetime. Moreover, after Rindler transformation, this new vector is the normal Killing vector of the BTZ inner horizon. We reproduce all known results about the holographic entanglement entropy of Bondi-Metzner-Sachs invariant field theories, which are dual to the asymptotically flat spacetimes.
Highlights
One of the proposals for the holographic dual of asymptotically flat spacetimes is given by Refs. [1,2]
We proposed a holographic method for the calculation of BMSinvariant field theories (BMSFT) entanglement entropy, which does not use the Rindler method and takes a flat-space limit from the calculations of the anti-de Sitter (AdS)=conformal field theory (CFT) correspondence
(ii) For the asymptotically AdS metric and its corresponding interval, we can use Ryu and Takayanagi (RT) prescription or its generalizations to gain an extremal curve in bulk, the length of which is proportional to the entanglement entropy of the interval
Summary
One of the proposals for the holographic dual of asymptotically flat spacetimes is given by Refs. [1,2]. To bypass Rindler transformation and introduce a method that solely uses the extremality condition, we use the bulk modular flow of the corresponding interval in the AdS case It vanishes on the RT extremal curve and transforms into the Killing vector normal to the outer horizon after Rindler transformation. The flat-space limit of our new vector field in the asymptotically AdS spacetime yields the bulk modular flow of the corresponding interval introduced in Ref. We can bypass Rindler transformation in this way by starting from the bulk modular flow of the original interval in the AdS case and constructing a new vector field by using the Killing equations, normality condition, and norm condition. The last section is devoted to the summary and conclusion
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
