Details
| Original language | English |
|---|---|
| Article number | 154 |
| Journal | Journal of High Energy Physics |
| Volume | 2020 |
| Issue number | 4 |
| Publication status | Published - 23 Apr 2020 |
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.
Keywords
- AdS-CFT Correspondence, Conformal and W Symmetry, Conformal Field Theory, Discrete Symmetries
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of High Energy Physics, Vol. 2020, No. 4, 154, 23.04.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dynamics for holographic codes
AU - Osborne, Tobias J.
AU - Stiegemann, Deniz E.
N1 - 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
PY - 2020/4/23
Y1 - 2020/4/23
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Conformal and W Symmetry
KW - Conformal Field Theory
KW - Discrete Symmetries
UR - http://www.scopus.com/inward/record.url?scp=85083840406&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1706.08823
DO - 10.48550/arXiv.1706.08823
M3 - Article
AN - SCOPUS:85083840406
VL - 2020
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 4
M1 - 154
ER -