Entanglement entropy, trace anomalies and holography

Schwimmer, A.; Theisen, Stefan

doi:10.1016/j.nuclphysb.2008.04.015

Cited by 147 publications

(188 citation statements)

References 29 publications

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“…Or, is there any hidden constraint from the entanglement entropy that forbids the R 2 term in the trace anomaly (see e.g. [56][57] for the Wess-Zumino consistency condition of the holographic renormalization and entanglement entropy)? In order to address these questions, it seems urgent to reconsider the holographic approach to the entanglement entropy [58][53] [55] in foliation preserving diffeomorphic theories of gravity.…”

Section: Discussionmentioning

confidence: 99%

Holographic renormalization of foliation preserving gravity and trace anomaly

Nakayama¹

2012

Gen Relativ Gravit

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From the holographic renormalization group viewpoint, while the scale transformation plays a primary role in holographic dualities by providing the extra dimension, the special conformal transformation seems to only play a secondary role.We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomorphic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomorphic theory of gravity could be in conflict with a theorem of the dual unitary quantum field theory.

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Section: Discussionmentioning

confidence: 99%

Holographic renormalization of foliation preserving gravity and trace anomaly

Nakayama¹

2012

Gen Relativ Gravit

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“…In this subsection, we introduce an elegant approach [46], which rests on the so-called Penrose-Brown-Henneaux (PBH) transformations, for the derivations of the universal terms of EE for CFTs. Taking advantage of the bulk diffeomorphisms and the reparametrization of the world volume (entropy functional), [46] finds that one do not need to solve equations of motion and the extremal entropy surface in order to derive the universal terms of EE for 4d CFTs.…”

Section: Approach Based On Pbh Transformationmentioning

confidence: 99%

“…Taking advantage of the bulk diffeomorphisms and the reparametrization of the world volume (entropy functional), [46] finds that one do not need to solve equations of motion and the extremal entropy surface in order to derive the universal terms of EE for 4d CFTs. As we shall show in section 4, this is also the case for 6d CFTs.…”

Section: Approach Based On Pbh Transformationmentioning

confidence: 99%

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Universal terms of entanglement entropy for 6d CFTs

Miao

2015

J. High Energ. Phys.

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Abstract:We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of [37,38]. Remarkably, we find that the holographic and the field theoretical results match exactly for the C 2 and Ck 2 terms, where C and k denote the Weyl tensor and the extrinsic curvature, respectively. As for the k 4 terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical k 4 terms match. Since we have much more equations than the free parameters, the match for k 4 terms is non-trivial.

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“…The a coefficients holographically computed in the Einstein-Hilbert gravity are known to be [15][16][17][18] …”

Section: Holographic Proof Of Thef -Theoremmentioning

confidence: 99%

Holographic interpolation between a and F

Kawano

Nakaguchi

Nishioka

2014

J. High Energ. Phys.

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An interpolating functionF between the a-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension d. We examineF in the large-N CFT's in d dimensions holographically described by the Einstein-Hilbert gravity in the AdS d+1 space. We show thatF is a smooth function of d and correctly interpolates the a coefficients and the free energies. The monotonicity ofF along an RG flow follows from the analytic continuation of the holographic c-theorem to continuous d, which completes the proof of the conjecture.

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Entanglement entropy, trace anomalies and holography

Cited by 147 publications

References 29 publications

Holographic renormalization of foliation preserving gravity and trace anomaly

Holographic renormalization of foliation preserving gravity and trace anomaly

Universal terms of entanglement entropy for 6d CFTs

Holographic interpolation between a and F

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