Holography and the future tube

Gibbons, G. W.

doi:10.1088/0264-9381/17/5/316

Cited by 10 publications

(12 citation statements)

References 22 publications

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“…The symplectic structure of timelike geodesics in AdS 3 has been considered in [50] and the relevant coadjoint orbits and their quantization have been discussed in many references including [26]. Here, we provide a summary and make an explicit connection between the two.…”

Section: A Timelike Geodesicsmentioning

confidence: 99%

Kinematic space and the orbit method

Penna

Zukowski

2019

J. High Energ. Phys.

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Kinematic space has been defined as the space of codimension-2 spacelike extremal surfaces in anti de Sitter (AdS d+1 ) spacetime which, by the Ryu-Takayanagi proposal, compute the entanglement entropy of spheres in the boundary CFT d . It has recently found many applications in holography. Coadjoint orbits are symplectic manifolds that are the classical analogues of a Lie group's unitary irreducible representations. We prove that kinematic space is a particular coadjoint orbit of the d-dimensional conformal group SO(d, 2). In addition, we show that the Crofton form on kinematic space associated to AdS 3 , that was shown to compute the lengths of bulk curves, is equal to the standard Kirillov-Kostant symplectic form on the coadjoint orbit. Since kinematic space is Kähler in addition to symplectic, it can be quantized. The orbit method extends the kinematic space dictionary, which was originally motivated through connections to integral geometry, by directly translating geometrical properties of holographic auxiliary spaces into statements about the representation theory of the conformal group.

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Section: A Timelike Geodesicsmentioning

confidence: 99%

Kinematic space and the orbit method

Penna

Zukowski

2019

J. High Energ. Phys.

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“…Its Shilov boundary Shilov (D 4 ) = Q 4 has precisely the same topology as the 4D conformally compactified real Minkowski space-time Q 4 ϭ M 4 ϭ ͑S 3 × S 1 ͒/Z 2 ϭ S 3 × RP 1 . For more details about Shilov boundaries, the conformal group, future tubes, and holography we refer to the article by Gibbons [2,70,74].…”

Section: Evaluation Of the Coupling Constantsmentioning

confidence: 99%

“…A study of Shilov boundaries, holography, and the future tube can be found in ref. 74. Furthermore, to resolve the scaling problems of Wyler's expression raised by Robertson, Gilmore showed why it is essential to use dimensionless volumes by setting the throat sizes of the anti-de Sitter hyperboloids to r = 1, because this is the only choice for r where all elements in the bounded domains are also coset representatives, and therefore, amount to honest group operations.…”

Section: ϫ2mentioning

confidence: 99%

A Clifford algebra-based grand unification program of gravity and the Standard Model: a review study

Castro

2014

Can. J. Phys.

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A Clifford Cl(5, C) unified gauge field theory formulation of conformal gravity and U(4) × U(4) × U(4) Yang-Mills in 4D, is reviewed along with its implications for the Pati-Salam (PS) group SU(4) × SU(2) L × SU(2) R , and trinification grand unified theory models of three fermion generations based on the group SU(3) C × SU(3) L × SU(3) R . We proceed with a brief review of a unification program of 4D gravity and SU(3) × SU(2) × U(1) Yang-Mills emerging from 8D pure quaternionic gravity. A realization of E 8 in terms of the Cl(16) = Cl(8) R Cl(8) generators follows, as a preamble to F. Smith's E 8 and Cl(16) = Cl(8) R Cl(8) unification model in 8D. The study of chiral fermions and instanton backgrounds in CP 2 and CP 3 related to the problem of obtaining three fermion generations is thoroughly studied. We continue with the evaluation of the coupling constants and particle masses based on the geometry of bounded complex homogeneous domains and geometric probability theory. An analysis of neutrino masses, Cabbibo-Kobayashi-Maskawa quark-mixing matrix parameters, and neutrino-mixing matrix parameters follows. We finalize with some concluding remarks about other proposals for the unification of gravity and the Standard Model, like string, M, and F theories and noncommutative and nonassociative geometry. Résumé : Nous passons en revue une formulation en théorie du champ unifié de Clifford Cl(5, C) de la gravité conforme et de Yang-Mills U(4) × U(4) × U(4) en 4D, avec ses implications pour le groupe de Pati-Salam SU(4) × SU(2) L × SU(2) R et les modèles GUT de trinification de trois générations de fermions basés sur le groupe SU(3) C × SU(3) L × SU(3) R . Nous commençons avec une brève revue du programme d'unification de la gravité 4D et Yang-Mills SU(3) × SU(2) × U(1) qui émerge de la gravité quaternionique pure en 8D. Nous poursuivons avec une réalisation de E 8 en termes des générateurs de Cl(16) = Cl(8) R Cl(8), comme introduction au modèle d'unification de F. Smith E 8 et Cl(16) = Cl(8) R Cl(8) en 8D. Nous étudions en profondeur les fermions chiraux et les fonds d'instantons dans CP 2 et CP 3 reliés à la difficulté d'obtenir trois générations de fermions. Nous continuons avec l'évaluation des constantes de couplage et des masses des particules, sur la base de la géométrie des domaines homogènes complexes bornés et de la théorie de probabilité géométrique. Suit une étude des masses des neutrinos, des paramètres de la matrice de mélange de Cabbibo-Kobayashi-Maskawa et des paramètres de la matrice d'oscillation de neutrinos. Nous concluons avec des remarques sur les propositions faites pour unifier la gravité et le modèle standard, comme la théorie des cordes, la théorie M et F, et la géométrie non associative et non commutative. [Traduit par la Rédaction]

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“…[P ],m = m(|P | − 1) − P 2 /4. 19 The detailed fusion rules between generic massive representations are complicated, although bound to be of the form (3.59), given the validity of composition and distribution rules in (3.41) and (3.42). thus describe singletons for |P | = 1, and massless as well as massive ground states with minimal conformal weight for |P | > 1.…”

Section: On Massive Sector and Realization Of Spectral Flowmentioning

confidence: 99%

“…The model nonetheless contains non-unitary and non-topological states. Drawing on the continuum limit of discretized branes [15] as well as on the sigmamodel description of null surfaces in anti-de Sitter spacetime [17] (see also [18,19]), it makes sense to entertain the idea that the coset model based on…”

Section: Introductionmentioning

confidence: 99%

On singleton composites in non-compact WZW models

Engquist¹,

Sundell²,

Tamassia³

2007

J. High Energy Phys.

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We examine the so(2, D − 1) WZW model at the subcritical level −(D − 3)/2. It has a singular vacuum vector at Virasoro level 2. Its decoupling constitutes an affine extension of the equation of motion of the (D + 1)-dimensional conformal particle, i.e. the scalar singleton. The admissible (spectrally flowed) representations contain the singleton and its direct products, consisting of massless and massive particles in AdS D . In D = 4 there exists an extended model containing both scalar and spinor singletons of sp(4). Its realization in terms of 4 symplectic-real bosons contains the spinor-oscillator constructions of the 4D singletons and their composites. We also comment on the prospects of relating gauged versions of the models to the phase-space quantization of partonic branes and higher-spin gauge theory.

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Holography and the future tube

Abstract: The Future Tube T

Cited by 10 publications

References 22 publications

Kinematic space and the orbit method

Kinematic space and the orbit method

A Clifford algebra-based grand unification program of gravity and the Standard Model: a review study

On singleton composites in non-compact WZW models

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