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Bulk entanglement entropy in perturbative excited states

by Alexandre Belin, Nabil Iqbal, Sagar F. Lokhande

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$_3$.

Current status:

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 (5 September 2018)
Submission 1805.08782v2 (28 June 2018)

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