Dynamics for holographic codes
- authored by
- Tobias J. Osborne, Deniz E. Stiegemann
- Abstract
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.
- Organisation(s)
-
Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
- External Organisation(s)
-
University of Queensland
- Type
- Article
- Journal
- Journal of High Energy Physics
- Volume
- 2020
- ISSN
- 1126-6708
- Publication date
- 23.04.2020
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.1706.08823 (Access:
Open)
https://doi.org/10.1007/JHEP04(2020)154 (Access: Open)