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 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 (ℝ1,1). The bulk Hilbert space is realised as a special subspace of the semicontinuous limit Hilbert space 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 given by a unitary representation of the Ptolemy group Pt , on the bulk Hilbert space thus realising a toy model of the AdS/CFT correspondence which we call the Pt /T correspondence.
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ArXiv ePrint: 1706.08823
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Osborne, T.J., Stiegemann, D.E. Dynamics for holographic codes. J. High Energ. Phys. 2020, 154 (2020). https://doi.org/10.1007/JHEP04(2020)154
- AdS-CFT Correspondence
- Discrete Symmetries
- Conformal and W Symmetry
- Conformal Field Theory