Abstract
We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle state in a scalar field theory in AdS_33. 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 cc. 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_33.
Highlights
We will be interested in calculating entanglement entropies in two-dimensional conformal field theories, which we describe in more detail
We will denote the bulk state with this metric and with the scalar field in their ground state by |0〉; this is dual to the vacuum of the CFT on S1 ×
We studied one-particle states in the bulk scalar free field theory, for which we computed the change in the minimal area as well as the bulk entanglement entropy
Summary
Large N and strong/weak dualities typically map quantum features of a given theory to classical structures in its dual. The latter turns out to be a non-trivial exercise in bulk quantum field theory, as the spatial spread of the φ wavefunction polarizes the entanglement already present in the vacuum, creating extra entanglement across the bulk of AdS3 We compute this shift in entanglement entropy by explicitly constructing the perturbative reduced density matrix in the excited state, decomposing the action of the single-particle creation operator a† across the entangling region ΣA and its complement. In principle our techniques allow an explicit computation for all θ , but in practice we were unable to perform the required analytic continuations away from the small θ limit, and so we express our final answers as an expansion in interval size Both from the bulk and boundary, we find the leading difference in entanglement entropy between the vacuum and the excited state to be:. Details of the computation of the Bogoliubov coefficients are relegated to an Appendix
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