Variational methods in AdS/CFT correspondence

Andrade, Tomás; Bañados, Máximo; Rojas, Francisco

doi:10.1103/physrevd.75.065013

Cited by 13 publications

(16 citation statements)

References 39 publications

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“…7 In the context of black holes and the AdS-CFT correspondence similar variational methods were used to properly regularize and renormalize black hole solutions [109]. 8 In the context of "bi-metric" truncations, (5.3) implies thatḡ selfcon k solves the tadpole equation.…”

Section: State Counting Based On γ Kmentioning

confidence: 99%

Black holes within asymptotic safety

Koch

Saueressig

2014

Int. J. Mod. Phys. A

119

118

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Black holes are probably among the most fascinating objects populating our universe. Their characteristic features found within general relativity, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. We review the status of black holes within a particular proposal for quantum gravity, Weinberg's asymptotic safety program. Starting from a brief survey of the effective average action and scale setting procedures, an improved quantum picture of the black hole is developed. The Schwarzschild black hole and its generalizations including angular momenta, higher-derivative corrections and the implications of extra dimensions are discussed in detail. In addition, the quantum singularity emerging for the inclusion of a cosmological constant is elucidated and linked to the phenomenon of a dynamical dimensional reduction of spacetime.

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Section: State Counting Based On γ Kmentioning

confidence: 99%

Black holes within asymptotic safety

Koch

Saueressig

2014

Int. J. Mod. Phys. A

119

118

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“…Equivalently said, the divergent terms in a variation of an action have to be represented as total variations of local terms integrated over boundary. In general, the computation of the total variation can be substantially simplified after noting that the conditions for the application of the theorem [19] are fulfilled in our case. For an alternative proof of the theorem [19], see appendix C. The theorem [19] states that the terms which are asymptotically divergent or zero (when ρ → 0) can always be represented as total variations of local boundary functionals.…”

Section: -Point Functionsmentioning

confidence: 99%

“…The conservation law for local Weyl transformations can be read off from Eq. (3.2c) as 19) where e a τ a is the trace of energy-momentum tensor, so A is also called the trace anomaly. Using the field equations and discarding the total divergence, one can show that the trace anomaly has the form…”

Section: Anomaliesmentioning

confidence: 99%

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Holography in Lovelock Chern-Simons AdS gravity

2017

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We analyse holographic field theory dual to Lovelock Chern-Simons AdS Gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level. IntroductionThe AdS/CFT correspondence [1] relates the fields in (d + 1)-dimensional asymptotically anti-de Sitter (AAdS) space and correlators in a d-dimensional Conformal Field Theory (CFT). These two theories are dual in the asymptotic sector of gravity, such that the weak coupling regime of one is related to the strong coupling regime of another. For a weak gravitational coupling, the bulk theory is well-described by its semiclassical approximation, leading to the form of the duality most often used.Since its discovery, the correspondence tools have been applied to many strongly coupled systems, giving rise to new insights into their dynamics, for example in hydrodynamics [2] and condensed matter systems such as superconductors [3].On the other hand, much effort has been invested in analysing the duality in semiclassical approximation of a bulk theory, with twofold purpose. First, it enables to test the conjecture itself. Second, it helps us to gain the knowledge about strongly coupled systems which are non-perturbative and not very well understood. However, most of this investigation deals with Riemannian geometry of bulk spacetime, see for example [3,4,5,6,7,8], while a more general structure based on Riemann-Cartan geometry, where both torsion and curvature determine gravitational dynamics, is mostly underinvestigated. One of the first * Email addresses: olivera.miskovic@pucv.cl, cbranislav@ipb.ac.rs, dsimic@ipb.ac.rs 1 studies of Riemann-Cartan holography used first order formalism to obtain a holographic dual of Chern-Simons AdS gravity in five dimensions [9]. After that, in three dimensions, holographic dual to the Mielke-Baekler model was analysed in [10], and to the most general parity-preserving three-dimensional gravity with propagating torsion in [11]. The physical interpretation of torsional degrees of freedom as carriers of a non-trivial gravitational magnetic field in 4D Einstein-Cartan gravity was discussed in [12].Studying holographic duals of gravity with torsion has many benefits. Since its setup is more general, it also contains the results of torsion-free gravity. One of the very important features is that treating vielbein and spin connection as independent dynamical variables simplifies calculations to great extent. In Ref.[11], it was shown that for three dimensional bulk gravity conservation laws of the boundary theory take the same form in RiemannCartan and Riemannian theory when the boundary torsion is set to zero. Thus, i...

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“…Notice, also, that both fields Φ 0 and Π 0 have spin zero (h Φ 0 − hΦ 0 = h Π 0 − hΠ 0 = 0). In addition, from (44)…”

Section: Now We Laurent Expandmentioning

confidence: 99%

A Note on Scalar Field Theory in AdS_3/CFT_2

Minces

2009

Preprint

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We consider a scalar field theory in AdS d+1 , and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions ∆ − and ∆ + , respectively, where ∆ ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS 3 /CF T 2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

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Variational methods in AdS/CFT correspondence

Cited by 13 publications

References 39 publications

Black holes within asymptotic safety

Black holes within asymptotic safety

Holography in Lovelock Chern-Simons AdS gravity

A Note on Scalar Field Theory in AdS_3/CFT_2

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