Bulk entanglement entropy in perturbative excited states

TL;DR

This paper calculates bulk entanglement entropy for a one-particle state in AdS3, confirming holographic formulas and providing explicit expressions for scalar field Bogoliubov coefficients, thus advancing understanding of quantum corrections in holography.

Contribution

It offers the first direct bulk calculation of entanglement entropy in a perturbative excited state, validating holographic quantum correction formulas beyond symmetry constraints.

Findings

Agreement with CFT entanglement entropy in excited states

Explicit formulas for scalar Bogoliubov coefficients

Validation of FLM and JLMS quantum correction formulas

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$_3$.