Dynamics for holographic codes

• Main Authors: Tobias J. Osborne, Deniz E. Stiegemann
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Discrete Symmetries; Conformal and W Symmetry; Conformal Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2020)154

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.