Stability at a local maximum in higher dimensional anti-deSitter space and applications to supergravity

Mezincescu, Luca; Townsend, Paul

doi:10.1016/0003-4916(85)90150-2

Cited by 184 publications

(236 citation statements)

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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: 93%

“…Thus, at first sight, it seems that the AdS/CFT prescription Eqs. (1, 12) successfully maps to the boundary all the information obtained in [33][34] [39] on performing the quantization of the scalar field theory on the AdS bulk. However, one of the purposes of this work is to point out that there remain some open problems which need to be considered.…”

Section: Motivationsmentioning

confidence: 99%

“…In spite of the fact that the regular solution has been much more studied than the irregular one, both of them exist and lead to consistent formulations. It is also important to point out that stability imposes the condition that ν (0) is a real number [33][34] [39]. Such a condition can be written as…”

Section: Motivationsmentioning

confidence: 99%

“…In order for the 'conserved' metrical energy to be actually conserved, Breitenlohner and Freedman impose that there is no flux of the current Eq. (25) through the boundary (see also [39] for the extension to the d+1 dimensional case), and this restriction fixes further conditions on the solution of the equation of motion. The result is that, whereas for regular modes the metrical energy is actually conserved for any value of , for irregular modes it is conserved only for being a solution of the constraint = 1 2…”

Section: Motivationsmentioning

confidence: 99%

“…(1) and the Legendre transform prescription in [38], gives rise to a consistent formulation of the scalar field theory on AdS spaces and in the AdS/CFT correspondence. However, we will show in this article that the usual quantization in global coordinates, as developed in [33][34] [39], imposes constraints on the mass and the coupling coefficient of the field to the metric which cannot be mapped to the boundary through the usual Dirichlet and Legendre transform prescriptions. It is a serious drawback, because the very first thing that we require on any AdS/CFT prescription is that it must be able to map to the boundary all the information contained in the AdS bulk.…”

Section: Introductionmentioning

confidence: 99%

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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: 93%

Section: Motivationsmentioning

confidence: 99%