Abstract
Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem. We consider a one-particle excited state of a massive scalar field infalling in a pure AdS3 geometry and compute these corrections for bulk subregions anchored on the AdS boundary. In the dual CFT2, the state is given by the insertion of a local primary operator and its evolution thereafter. We calculate the area and bulk entanglement entropy corrections at order mathcal{O}left({N}^0right), both in AdS and its CFT dual. The two calculations match, thus providing a non-trivial check of the FLM formula in a dynamical setting. Further, we observe that the bulk entanglement entropy follows a Page curve. We explain the precise sense in which our setup can be interpreted as a simple model of black hole evaporation and comment on the implications for the information problem.
Highlights
1.1 The big pictureThe presence of entanglement is an essential and ubiquitous feature of quantum systems
Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem
We consider a one-particle excited state of a massive scalar field infalling in a pure AdS3 geometry and compute these corrections for bulk subregions anchored on the AdS boundary
Summary
The presence of entanglement is an essential and ubiquitous feature of quantum systems. One of the precise entries in holographic dictionary is the statement that the entanglement entropy of a subregion A in the dual CFT is equal to the area of an extremal codimension-two surface γAext anchored at the boundary of AdS and homologous to the subregion A [5] This is known as the RT/HRT formula and the extremal surface γAext is often referred to as the RT surface. The entanglement entropy is given in terms of a different extremal surface γAext called quantum extremal surface so that min γAext ext γA This new prescription agrees with FLM at order O(1), but generalizes it to all orders in G. The implementation of (1.4) would require understanding of the bulk entanglement entropy for general regions, a task that is very difficult to accomplish in practice, in higher than two bulk dimensions These proposals highlight the utility of holography in the study of non-perturbative aspects of the black hole information paradox. We will show that we can interpret our setup as a simple toy model for black hole evaporation, providing fresh insight on the black hole information problem
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