We propose a discretization of the AdS/CFT correspondence with bulk space the $p$-adic Bruhat-Tits trees.
In addition to a consistent description of field theory on the boundary and gravity on the bulk, this approach
allows for a natural interpretation of the more recent viewpoint on holography, where bulk geometry emerges
from quantum entanglement on the boundary, in terms of a construction of holographic classical and quantum
codes on the Bruhat-Tits trees.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/6826