Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

Sumit R. Das, Anurag Kaushal, Gautam Mandal, Kanhu Kishore Nanda, Mohamed Hany Radwan, Sandip P. Trivedi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study minimum area surfaces associated with a region, R, of an internal space. For example, for a warped product involving an asymptotically AdS space and an internal space K, the region R lies in K and the surface ends on ∂R. We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region R. When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory. We study several examples, including warped or direct products involving AdS 2, or higher dimensional AdS spaces, with the internal space, K = R m , S m; Dp brane geometries and their near horizon limits; and several geometries with a UV cut-off. We find that such RT surfaces often exist and can be useful probes of the system, revealing information about finite length correlations, thermodynamics and entanglement. We also make some preliminary observations about the role such surfaces can play in bulk reconstruction, and their relation to subalgebras of observables in the boundary theory.

Original languageEnglish
Article number141
JournalJournal of High Energy Physics
Volume2023
Issue number4
DOIs
StatePublished - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Keywords

  • AdS-CFT Correspondence
  • D-Branes
  • Gauge-Gravity Correspondence

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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