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)