Lecture 11: Aspects of the AdS Hilbert Space
In this lecture, we considered some aspects of the Hilbert space of QFTs and gravity in AdS. We started by considering a minimally coupled scalar in AdS. We found that the Hilbert space could be constructed by exciting the vacuum with asymptotic operators smeared over boundary regions. We then found that this description continues to hold wheninteractions are turned on, and even in theories of gravity. This description of the Hilbert space is overcomplete but it automatically includes black holes formed from collapse and other states that we usually think of as being "nonperturbative".
Finally, we found that the same Hilbert space could also be obtained by acting with asymptotic operators smeared over a time band of size $\epsilon$. This last result is a simple version of the Reeh-Schlieder theorem that applies even to theories of gravity.
