The factorization puzzle and its possible resolutions

Spacetime wormholes have been crucial in the recent understanding of the physics of quantum black holes. However, existence of wormholes lead to the factorization problem, which refers to the fact that if a wormhole links two boundary systems (denoted by L and R) in AdS/CFT context, the total partition function fails to factorize. We will first  look into the origin of this puzzle, and then we will move on to the possible ways of resolution of this puzzle. In this context, we will briefly review the factorization in the one-time SYK (Sachdev-Ye-Kitaev) model and how the appearance of new saddle points help resolve this issue. Then we will focus on how the factorization properties change under irrelevant deformations of the theory, i.e, how the deformations affect the saddles and what these deformations amount to in case of the one-time and two-time version of the SYK theory.