Renormalized entanglement entropy
Renormalized entanglement entropy
We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in AdS4 spacetimes agrees precisely with the holographically renormalized action for AdS4 with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension 3/2 < Δ < 5/2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.
1-42
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Woodhead, William
2af6629c-0b18-47cf-b751-975beb5e5652
29 August 2016
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Woodhead, William
2af6629c-0b18-47cf-b751-975beb5e5652
Taylor, Marika and Woodhead, William
(2016)
Renormalized entanglement entropy.
Journal of High Energy Physics, 2016 (165), .
(doi:10.1007/JHEP08(2016)165).
Abstract
We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in AdS4 spacetimes agrees precisely with the holographically renormalized action for AdS4 with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension 3/2 < Δ < 5/2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.
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1604.06808.pdf
- Accepted Manuscript
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art_10.1007_JHEP08(2016)165.pdf
- Version of Record
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Accepted/In Press date: 24 August 2016
e-pub ahead of print date: 29 August 2016
Published date: 29 August 2016
Organisations:
Applied Mathematics
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Local EPrints ID: 400427
URI: http://eprints.soton.ac.uk/id/eprint/400427
PURE UUID: 5aa909b6-b9b4-41f1-a4c2-20e947f54f28
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Date deposited: 16 Sep 2016 10:28
Last modified: 22 Aug 2025 02:06
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Author:
William Woodhead
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