Bulk entanglement entropy for photons and gravitons in AdS$_3$

Belin, Alexandre; Iqbal, Nabil; Kruthoff, Jorrit

Abstract

We study quantum corrections to holographic entanglement entropy in AdS3/CFT2; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk U(1) gauge fields and gravitons, whose dynamics in AdS3 are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton’s constant. We also consider excited states obtained by acting with the U(1) current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.

Citation

Belin, A., Iqbal, N., & Kruthoff, J. (2020). Bulk entanglement entropy for photons and gravitons in AdS$_3$. SciPost Physics, 8(5), Article 075. https://doi.org/10.21468/scipostphys.8.5.075

• Journal Article Type: Article
• Acceptance Date: Apr 24, 2020
• Online Publication Date: May 13, 2020
• Publication Date: 2020-05
• Deposit Date: May 13, 2020
• Publicly Available Date: Jun 18, 2020
• Journal: SciPost Physics.
• Print ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 5
• Article Number: 075
• DOI: https://doi.org/10.21468/scipostphys.8.5.075
• Related Public URLs: https://arxiv.org/abs/1912.00024