How does the holographic principle explain the emergence of bulk locality in AdS/CFT?

Question

I've been reading up on the holographic principle and the AdS/CFT correspondence, and I've hit a bit of a conceptual roadblock that I'm hoping someone can help me with.

In the AdS/CFT correspondence, we're told that a gravity theory in a higher-dimensional Anti-de Sitter (AdS) space is equivalent to a conformal field theory (CFT) on its lower-dimensional boundary. That sounds fascinating, but here's where I'm confused: if the boundary theory doesn't include gravity and is in fewer dimensions, how does it capture the local physics of the bulk AdS space?

Specifically:

How does bulk locality emerge from the boundary CFT? If all the dynamics are encoded on the boundary, how can we talk about events happening at specific points in the higher-dimensional bulk space? Is bulk locality an emergent phenomenon in this framework? Does it arise naturally from the boundary theory, or is there some additional structure or mechanism that makes this happen? Can someone provide an intuitive explanation or point me toward resources that clarify this? I've come across terms like "entanglement wedge reconstruction" and the Ryu-Takayanagi formula relating entanglement entropy to geometric surfaces in AdS, but I'm still having trouble seeing the big picture. I'm trying to wrap my head around how a lower-dimensional theory without gravity can fully represent a higher-dimensional gravitational theory, especially when it comes to local interactions in the bulk.

Any insights or explanations would be greatly appreciated!

This post imported from StackExchange Physics at 2024-10-05 20:59 (UTC), posted by SE-user Arham Zahid

Comments

Asking how you can tell that a CFT is compatible with bulk locality is a bit like asking how you can tell that QCD confines. Most progress that has been made is incremental.

This post imported from StackExchange Physics at 2024-10-05 20:59 (UTC), posted by SE-user Connor Behan