Quantum field theory in anti-de Sitter space-time

Avis, S. J.; Isham, C. J.; Storey, D.

doi:10.1103/physrevd.18.3565

Cited by 446 publications

(710 citation statements)

References 13 publications

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“…A consistent quantization of a massive real scalar field theory on AdS 4 was found in [33][34] (see also [40] for earlier results) and then extended to AdS d+1 in [39]. It will be useful to begin by concentrating on the minimally coupled case.…”

Section: Motivationsmentioning

confidence: 99%

“…The analysis in [33][34] is based on a previous formulation in [40][42] and, in particular, it defines the contribution of the scalar field to the energy of the system as the 'conserved' charge corresponding to the conserved current…”

Section: Motivationsmentioning

confidence: 99%

“…The solution proposed in [33][34] [40] for performing a consistent quantization was to compactify the space and impose appropriate boundary conditions on the solution of the classical equation of motion, such as the scalar product Eq. (4) be actually conserved.…”

Section: Motivationsmentioning

confidence: 99%

“…In the formulation of [33][34] [40], the solution of the classical equation of motion of the scalar field (∇ 2 − m 2 ) φ = 0 is expanded in modes…”

Section: Motivationsmentioning

confidence: 99%

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Energy and the AdS/CFT correspondence

Minces

Rivelles

2001

J. High Energy Phys.

144

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We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for 'regular' and 'irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformal dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

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Section: Motivationsmentioning

confidence: 99%

Section: Motivationsmentioning

confidence: 99%

Section: Motivationsmentioning

confidence: 99%

“…In the formulation of [33][34] [40], the solution of the classical equation of motion of the scalar field (∇ 2 − m 2 ) φ = 0 is expanded in modes…”

Section: Motivationsmentioning

confidence: 99%

See 2 more Smart Citations

Energy and the AdS/CFT correspondence

Minces

Rivelles

2001

J. High Energy Phys.

144

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“…Of course, combined Ω 2 → −Ω 2 , this corresponds precisely to the classification under parity discussed in section 3.1. This is the interacting version of the two quantization schemes discussed in [14] for the free field theory. The above will become crucial when we discuss quantization of these solutions later.…”

Section: Fluctuations Around the Bulk Instantonmentioning

confidence: 99%

Instantons and conformal holography

Haro

Petkou

2006

J. High Energy Phys.

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We study a subsector of the AdS 4 /CFT 3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a φ 4 potential, and is holographically related to a massless scalar with a φ 6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.

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Model of a relativistic oscillator in a generalized Schrödinger picture

Frick

2011

Annalen der Physik

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In a generalized Schrödinger picture, we consider the motion of a relativistic particle in an external field (like in the case of a harmonic oscillator). In this picture the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the Anti de Sitter (AdS) space. We also consider the nonrelativistic limit.

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Quantum field theory in anti-de Sitter space-time

Cited by 446 publications

References 13 publications

Energy and the AdS/CFT correspondence

Energy and the AdS/CFT correspondence

Instantons and conformal holography

Model of a relativistic oscillator in a generalized Schrödinger picture

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