Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
Time: 10:00am (UTC/GMT+8:00, Beijing/Shanghai), Dec. 8 (Wed.) , 2021
Meeting ID: 825 1640 8425
Speaker: Kenta Suzuki (YITP)
Wormhole geometry gives several nice features for gravitational path integral, but also leads to some puzzles. In the context of the AdS/CFT correspondence, one of the puzzles is the factorization problem, which is intimately related to ensemble averaging
of the boundary theory.
In order to further study the nature of factorization in a simple set-up of the AdS/CFT correspondence, in this talk, we introduce a partially disorder-averaged SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields.These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop non-trivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary, and they play a crucial role for the factorization.