Gravity factorized

There are various aspects of the AdS/CFT correspondence that are rather mysterious. For example, how does the gravitational theory know about a discrete boundary spectrum or how does it know moments of the partition function factorize, given the existence of connected (wormhole) geometries? In this talk I will discuss some recent efforts with Andreas Blommaert and Luca Iliesiu on these two puzzles in two dimensional dilaton gravities. These gravity theories are simple enough that we can understand and propose a resolution to the discreteness and factorization puzzles. I will show that a tiny but universal bilocal spacetime interaction in the bulk is enough to ensure factorization, whereas modifying the dilaton potential with tiny corrections gives a discrete boundary spectrum. We will discuss the meaning of these corrections and how they could be related to resolutions of the same puzzles in higher dimensions.