# Dynamics for holographic codes

We describe how to introduce dynamics for the holographic states and codes introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the definition of a continuous limit of the kinematical Hilbert space of a finite H which we argue may be achieved via the semicontinuous limit of Jones. Dynamics is then introduced by building a unitary representation of a group known as Thompson's group T, which is closely related to the conformal group conf(R^1,1). The bulk Hilbert space is then realised as a special subspace of the semicontinuous limit H spanned by a class of distinguished states which can be assigned a discrete bulk geometry. The analogue of the group of large bulk diffeomorphisms is then given by a unitary representation of the Ptolemy group Pt, on the bulk Hilbert space thus realising a toy model of AdS/CFT which we call the Pt/T correspondence. This paper is primarily targeted at physicists, particularly, quantum information theorists, however mathematicians knowledgeable of circle groups and Thompson's groups F and T may find the paper helpful as a way to get a sense of the AdS/CFT correspondence.
Submitted 27 Jun 2017 to Quantum Physics [quant-ph]
Published 28 Jun 2017
Updated 8 Sep 2017
Author comments: 40 pages, 37 figures (small revisions). See video of related talk: https://www.youtube.com/watch?v=xc2KIa2LDFo
http://arxiv.org/abs/1706.08823
http://arxiv.org/pdf/1706.08823.pdf
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