Entanglement entropy for free scalar fields in AdS

Abstract

We compute entanglement entropy for free massive scalar fields in anti-de Sitter (AdS) space. The entangling surface is a minimal surface whose boundary is a sphere at the boundary of AdS. The entropy can be evaluated from the thermal free energy of the fields on a topological black hole by using the replica method. In odd-dimensional AdS, exact expressions of the Renyi entropy $S_n$ are obtained for arbitrary $n$. We also evaluate 1-loop corrections coming from the scalar fields to holographic entanglement entropy. Applying the results, we compute the leading difference of entanglement entropy between two holographic CFTs related by a renormalization group flow triggered by a double trace deformation. The difference is proportional to the shift of a central charge under the flow.

v3: 25 pages, 2 figures, typos corrected

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
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• Quantum Corrections to Holographic Mutual Information
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• Bulk entanglement entropy for photons and gravitons in AdS${}_3$
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• Target space entanglement in quantum mechanics of fermions and matrices
• On partition functions and phases of scalars in AdS
• Phases of theories with fermions in AdS
• Effects of Non-Conformal Boundary on Entanglement Entropy
• Entanglement entropy of non-local theories in AdS
• Bulk entanglement and its shape dependence
• Entanglement Entropy Evolution under Double-trace Deformation