Holographic renormalization of foliation preserving gravity and trace anomaly

Nakayama, Yu

doi:10.1007/s10714-012-1427-3

Cited by 15 publications

(14 citation statements)

References 67 publications

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“…as expected from the field theory Callan-Symanzik equation (33). Again, this result is equivalent to the holographic renormalizability of the Gubser-Klebanov-Polyakov-Witten partition function.…”

Section: Holographysupporting

confidence: 67%

“…Note that the unitarity seems crucial. One may find counter-examples once we discard the null energy-condition [30][31] [32] or the full space-time diffeomorphism [33] of the bulk theory.…”

Section: Holographymentioning

confidence: 99%

“…[11] [12] follows from (8) by using the renormalization group invariance of Schwinger's source functional The gradient formula (8) together with the claim thatâ(g) does not depend explicitly on…”

mentioning

confidence: 99%

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Vector Beta Function

Nakayama

2013

Int. J. Mod. Phys. A

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We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that non-renormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holography in the weakly coupled gravity regime.

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Section: Holographysupporting

confidence: 67%

“…Note that the unitarity seems crucial. One may find counter-examples once we discard the null energy-condition [30][31] [32] or the full space-time diffeomorphism [33] of the bulk theory.…”

Section: Holographymentioning

confidence: 99%

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Vector Beta Function

Nakayama

2013

Int. J. Mod. Phys. A

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“…Of course, this is the value that we would get in the Einstein-Hilbert action. It is related to the fact that we did not have bare R 2 term in the conformal anomaly from the holographic renormalization group viewpoint [31].…”

Section: Jhep06(2015)092mentioning

confidence: 99%

Local renormalization group functions from quantum renormalization group and holographic bulk locality

Nakayama

2015

J. High Energ. Phys.

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The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.

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“…The former statement means that in the presence of the e term, the right hand side of (23) could be considered as (generalized) Graham-Witten anomalies for a 2 dimensional submanifold on the D dimensional SFT. To check this proposition one could redo the machinery of Graham and Witten for non-AlAdS manifolds such as geometries in the foliation preserving diffeomorphic theory of gravity [51]. The point which should be stressed here is that S EE is a UV divergent quantity in a continuum QFT.…”

Section: Entanglement Entropy and Scale Vs Conformal-mentioning

confidence: 99%

Scale versus conformal invariance from entanglement entropy

Naseh

2016

Phys. Rev. D

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For a generic conformal field theory (CFT) in four dimensions, the scale anomaly dictates that the universal part of entanglement entropy across a sphere (Cuniv(S 2 )) is positive. Based on this fact, we explore the consequences of assuming positive sign for Cuniv(S 2 ) in a four dimensional scale invariant theory (SFT). In absence of a dimension two scalar operator O2 in the spectrum of a SFT, we show that this assumption suggests that SFT is a CFT. In presence of O2, we show that this assumption can fix the coefficient of the nonlinear coupling term d 4 x √ gRO2 to a conformal value.PACS numbers: 11.25.TqThe asymptotic structure of Poincaré invariant unitary quantum field theories in deep UV and IR is of great importance in physics. A deep understanding of this issue is achievable via the profound idea of Wilson [1]. According to this idea, the fixed points of renormalization group (RG) are dwellings of that asymptotics and therefore the asymptotic theories are scale invariant. Other new dwellings are the renormalization group limit cycles which also describe the scale invariant field theories. Remarkably, with a few known exceptions, unitary SFT's always exhibit full conformal symmetry. A natural question is whether it is possible for a theory to be scale invariant but not conformal invariant? The converse question, i.e., whether a theory can be invariant under conformal transformations but not under scaling, is easy to answer. The commutator between the conserved generators of translations and conformal transformations gives the scaling generator together with the Lorentz ones. This means that Poincaré plus conformal invariance comprises scale invariance. The converse is still an open question since Poincaré and scaling generators form a closed algebra.Recently there were considerable efforts to answer this question and the task has been done in some spacetime dimensions, but the problem is still open for D = 4. Although some comprehensive arguments are available in 4D, they still suffer from serious loophole. In this paper we study the problem of scale vs conformal invariance in 4D by making use of entanglement entropy. For a generic CFT in 4D, the scale anomaly dictates that the universal part of entanglement entropy across a sphere (C univ (S 2 )) is positive [2]. Based on this fact, we explore the consequences of assuming positive sign for C univ (S 2 ) in a 4D SFT. In absence of a dimension two scalar operator O 2 in the spectrum of a SFT, we show that this assumption suggests that the SFT actually is a CFT. In presence of O 2 , which is actually related to the loophole in previous studies, we show that this assumption fixes the coefficient of the nonlinear coupling term d 4 x √ gRO 2 to a conformal value.The paper is organized as follows. The first section is devoted to a comprehensive review on previous studies on the subject of scale vs conformal invariance by emphasizing on 4D. Since our work is highly based on using scale anomaly in SFTs we will dedicate some parts of the first section to this topi...

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Holographic renormalization of foliation preserving gravity and trace anomaly

Cited by 15 publications

References 67 publications

Vector Beta Function

Vector Beta Function

Local renormalization group functions from quantum renormalization group and holographic bulk locality

Scale versus conformal invariance from entanglement entropy

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