Bulk entanglement entropy in perturbative excited states

Submission summary

 As Contributors: Alexandre Belin · Nabil Iqbal · Sagar F. Lokhande Arxiv Link: https://arxiv.org/abs/1805.08782v3 (pdf) Date accepted: 2018-09-10 Date submitted: 2018-09-05 02:00 Submitted by: Lokhande, Sagar F. Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

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$_3$.

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Published as SciPost Phys. 5, 024 (2018)

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.