Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes

Understand

Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states.

• The coarse-graining procedure involves identifying degrees of freedom entangled at short distances and disentangling them.
• This is manifested in the bulk by a flow equation that generates a codimension-1 object, which we refer to as the holographic slice.
• We generalize the earlier classical construction to include bulk quantum corrections, which naturally involves the generalized entropy as a measure of the number of relevant boundary degrees of freedom.