Universal features of holographic anomalies

Schwimmer, A.; Theisen, Stefan

doi:10.1088/1126-6708/2003/10/001

Cited by 35 publications

(36 citation statements)

References 22 publications

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“…The effective theory we develop may have broader applications for the study of holographic phenomenology [27,28], where our methods could be used to derive both the universal anomaly matching terms and the conformally invariant terms for light dilatons. Our methods might also relate to 6 WhenM I 1 is far away from this central value, it will lead to ghosts or negligible mixing [36].…”

Section: Discussionmentioning

confidence: 99%

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An effective theory for holographic RG flows

Kaplan

Wang

2015

J. High Energ. Phys.

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We study the dilaton action induced by RG flows between holographic CFT fixed points. For this purpose we introduce a general bulk effective theory for the goldstone boson of the broken spacetime symmetry, providing an AdS analog of the EFT of Inflation. In two dimensions, we use the effective theory to compute the dilaton action, as well as the UV and IR conformal anomalies, without further assumptions. In higher dimensions we take a 'slow-flow' limit analogous to the assumption of slow-roll in Inflation, and in this context we obtain the dilaton action, focusing on terms proportional to the difference of the A-type anomalies. We include Gauss-Bonnet terms in the gravitational action in order to verify that our method correctly differentiates between A-type and other anomalies.

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Section: Discussionmentioning

confidence: 99%

“…Thus our approach may be viewed as intermediate between a general conformal symmetry analysis [5][6][7][8][9] and the study of particular holographic examples (see [10] for a review and many older references e.g. [11], and also the recent work [12][13][14][15]) for the study of the low-energy τ action.…”

Section: Jhep02(2015)056mentioning

confidence: 99%

An effective theory for holographic RG flows

Kaplan

Wang

2015

J. High Energ. Phys.

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“…In general, any spacetime metric can be put in Gaussnormal coordinates ds 2 = N 2 (ρ)dρ 2 + h ij (x, ρ)dx i dx j . For AAdS spaces in EGB gravity (3), the FeffermanGraham expansion of the metric is also valid and defined by N = ℓ eff /2ρ, h ij = g ij (x, ρ)/ρ and the expansion g ij = g (0)ij +ρg (1)ij +ρ 2 g (2)ij +..., where g (0) represents the metric of the conformal boundary ρ = 0 [11,12]. The extrinsic curvature K ij = −∂ ρ h ij /2N takes the form…”

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confidence: 99%

Vacuum energy in Einstein-Gauss-Bonnet anti–de Sitter gravity

Kofinas

Olea²

2006

Phys. Rev. D

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A finite action principle for Einstein-Gauss-Bonnet anti−de Sitter gravity is achieved supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, and to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.In recent years, several experiments carried out suggest observational evidence for a positive value of the cosmological constant [1]. Nonetheless, from a theoretical point of view, the idea of existence of extra dimensions and alternative gravity theories does not rule out a negative cosmological constant in a higher-dimensional spacetime. On the contrary, for example, particular braneworld models induce a zero or positive cosmological constant on a four-dimensional Universe [2]. A negative cosmological constant is also appealing because of the possibility of a profound connection between anti-de Sitter gravity and a conformal field theory (CFT) living on its boundary, that has attracted a considerable attention in the literature [3]. Even though some remarkable progress has been achieved on a rather case-by-case basis, a general proof of this duality remains unknown. In that context, the existence of a nonzero energy for anti-de Sitter (AdS) vacuum spacetime in the gravity side may be helpful to identify the corresponding CFT at the boundary. Indeed, in five dimensions, the matching between the zero-point energy for Schwarzschild-AdS black hole and the induced (Casimir) energy of a precise boundary field theory is one of the best known examples that realizes this bulk/boundary correspondence [4]. General Relativity with AdS asymptotics requires a regularization procedure in order to define a finite energy for the solutions of the theory. Logically, a vacuum energy can appear only when this mechanism does not invoke the substraction of a background configuration as, e.g., in Hamiltonian formalism. That is the case of the counterterms method [5,6], where the finiteness of the action and its energy-momentum tensor is obtained by the addition of covariant functionals of the boundary metric, constructed by solving the Einstein equations in a given asymptotic form of the metric [7]. In spite this algorithm provides the correct counterterms for many cases, in high enough dimension it becomes rather cumbersome, what makes the full series still unknown. It is clear that the inclusion of quadratic curvature terms in the action will turn this method of regularization even more complex.In this artic...

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“…In particular, in [22], general formulas for Asymptotically locally AdS spacetimes have been displayed. Dimensional regularization is also available with equivalent results [24,25,26]. A Hamilton-Jacobi method, exploiting the gravitational Hamiltonian constraint, is also available [27].…”

Section: Now the Approximation (4) Is Valid Provided The Action I[φ]mentioning

confidence: 99%

Variational methods in AdS/CFT correspondence

2007

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We prove that the AdS/CF T calculation of 1-point functions can be drastically simplified by using variational arguments. We give a simple proof, valid for any theory that can be derived from a Lagrangian, that the large radius divergencies in 1-point functions can always be renormalized away (at least in the semiclassical approximation). The renormalized 1-point functions then follow by a simple variational problem involving only finite quantities. Several examples, a massive scalar, gravity, and renormalization flows, are discussed. Our results are general and can thus be used for dualities beyond AdS/CF T .

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Universal features of holographic anomalies

Cited by 35 publications

References 22 publications

An effective theory for holographic RG flows

An effective theory for holographic RG flows

Vacuum energy in Einstein-Gauss-Bonnet anti–de Sitter gravity

Variational methods in AdS/CFT correspondence

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