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 (ℝ^1,1). 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)

BibTeX

@article{e96f2d43eccf4b24b1e5f2bb2c555055,
title = "Dynamics for holographic codes",
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{\textquoteright}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.",
keywords = "AdS-CFT Correspondence, Conformal and W Symmetry, Conformal Field Theory, Discrete Symmetries",
author = "Osborne, {Tobias J.} and Stiegemann, {Deniz E.}",
note = "Funding information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited",
year = "2020",
month = apr,
day = "23",
doi = "10.48550/arXiv.1706.08823",
language = "English",
volume = "2020",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "4",
}