We study quantum corrections to holographic entanglement entropy in AdS$_3$/CFT$_2$; 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 AdS$_3$ 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.
Cited by 4
Jackson R. Fliss et al., Interfaces and the extended Hilbert space of Chern-Simons theory
J. High Energ. Phys. 2020, 9 (2020) [Crossref]
Sumit R. Das et al., Gauge invariant target space entanglement in D-brane holography
J. High Energ. Phys. 2021, 225 (2021) [Crossref]
Daniel Kabat et al., Endpoint contributions to excited-state modular Hamiltonians
J. High Energ. Phys. 2020, 128 (2020) [Crossref]
Alexandre Belin et al., From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
J. High Energ. Phys. 2020, 185 (2020) [Crossref]
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- 1 Organisation européenne pour la recherche nucléaire / European Organization for Nuclear Research [CERN]
- 2 Durham University
- 3 Stanford University [SU]