# Bulk entanglement entropy in perturbative excited states

### Submission summary

 As Contributors: Sagar F. Lokhande Arxiv Link: https://arxiv.org/abs/1805.08782v3 Date accepted: 2018-09-10 Date submitted: 2018-09-05 Submitted by: Lokhande, Sagar F. Submitted to: SciPost Physics Domain(s): Theoretical Subject area: High-Energy Physics - Theory

### Abstract

We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle state in a scalar field theory in AdS$_3$. We work directly within the bulk Hilbert space and include the spatial spread of the scalar wavefunction. We give closed form expressions in the limit of small interval sizes and compare the result to a CFT computation of entanglement entropy in an excited primary state at large $c$. Including the contribution from the backreacted minimal area, we find agreement between the CFT result and the FLM and JLMS formulas for quantum corrections to holographic entanglement entropy. This provides a non-trivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closed-form expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS$_3$.

### Ontology / Topics

See full Ontology or Topics database.

### List of changes

1. Fixed a missing 1/n factor in equation (2.11). $theta$ now becomes $\theta/n$.
2. A typo in the definition of $z$ in equation (2.10) corrected and a few clarificatory words added just above this equation.
3. Forgotten factors of $\frac{1}{1-n}\log$ in equations (2.12), (2.15), (2.17) and (2.21) put in. These do not change any preceding or succeeding expressions.

### Submission & Refereeing History

Resubmission 1805.08782v3 on 5 September 2018
Submission 1805.08782v2 on 28 June 2018