skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Conformally related massless fields in dS, AdS and Minkowski spaces

Abstract

In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS), and Minkowski spacetimes in d dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and two-points functions, turns out to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.

Authors:
;  [1];  [2];  [1];  [2]
  1. APC, 11 pl. M. Berthelot, F-75231 Paris Cedex 05 (France)
  2. (France)
Publication Date:
OSTI Identifier:
20782924
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.73.084025; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONFORMAL INVARIANCE; DE SITTER GROUP; EINSTEIN FIELD EQUATIONS; MINKOWSKI SPACE; QUANTUM FIELD THEORY; SCALARS; SPACE-TIME; WAVE FUNCTIONS

Citation Formats

Huguet, E., Queva, J., Universite Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05, Renaud, J., and Universite de Marne la Vallee, 5 Bld Descartes, Champs sur marne, 77454 Marne-la-Vallee Cedex 2. Conformally related massless fields in dS, AdS and Minkowski spaces. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.084025.
Huguet, E., Queva, J., Universite Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05, Renaud, J., & Universite de Marne la Vallee, 5 Bld Descartes, Champs sur marne, 77454 Marne-la-Vallee Cedex 2. Conformally related massless fields in dS, AdS and Minkowski spaces. United States. doi:10.1103/PHYSREVD.73.084025.
Huguet, E., Queva, J., Universite Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05, Renaud, J., and Universite de Marne la Vallee, 5 Bld Descartes, Champs sur marne, 77454 Marne-la-Vallee Cedex 2. Sat . "Conformally related massless fields in dS, AdS and Minkowski spaces". United States. doi:10.1103/PHYSREVD.73.084025.
@article{osti_20782924,
title = {Conformally related massless fields in dS, AdS and Minkowski spaces},
author = {Huguet, E. and Queva, J. and Universite Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05 and Renaud, J. and Universite de Marne la Vallee, 5 Bld Descartes, Champs sur marne, 77454 Marne-la-Vallee Cedex 2},
abstractNote = {In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS), and Minkowski spacetimes in d dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and two-points functions, turns out to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.},
doi = {10.1103/PHYSREVD.73.084025},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
  • AdS waves and pp-waves can only be supported by pure radiation fields, for which the only nonvanishing component of the energy-momentum tensor is the energy density along the retarded time. We show that the nonminimal coupling of self-gravitating scalar fields to the higher-dimensional versions of these exact gravitational waves can be done consistently. In both cases, the resulting pure radiation constraints completely fix the scalar field dependence and the form of the allowed self-interactions. More significantly, we establish that the two sets of pure radiation constraints are conformally related for any nonminimal coupling, in spite of the fact that themore » involved gravitational fields are not necessarily related. In this correspondence, the potential supporting the AdS waves emerges from the self-interaction associated to the pp-waves and a self-dual condition naturally satisfied by the pp-wave scalar fields.« less
  • Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The Hilbert space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemannian manifold, presented first by Bros et al. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied inmore » the final stage.« less
  • Here, we extend our earlier work on the minimal unitary representation of SO(d, 2)and its deformations for d=4, 5and 6to arbitrary dimensions d. We show that there is a one-to-one correspondence between the minrep of SO(d, 2)and its deformations and massless conformal fields in Minkowskian spacetimes in ddimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep, and its enveloping algebra yields directly the standard bosonic AdS (d+1)/CFT d higher spin algebra. For deformed minrepsmore » the generators of certain deformations of Joseph ideal vanish as operators and their enveloping algebras lead to deformations of the standard bosonic higher spin algebra. In odd dimensions there is a unique deformation of the higher spin algebra corresponding to the spinor singleton. In even dimensions one finds infinitely many deformations of the higher spin algebra labelled by the eigenvalues of Casimir operator of the little group SO(d–2)for massless representations.« less
  • Here, we extend our earlier work on the minimal unitary representation of SO(d, 2)and its deformations for d=4, 5and 6to arbitrary dimensions d. We show that there is a one-to-one correspondence between the minrep of SO(d, 2)and its deformations and massless conformal fields in Minkowskian spacetimes in ddimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep, and its enveloping algebra yields directly the standard bosonic AdS (d+1)/CFT d higher spin algebra. For deformed minrepsmore » the generators of certain deformations of Joseph ideal vanish as operators and their enveloping algebras lead to deformations of the standard bosonic higher spin algebra. In odd dimensions there is a unique deformation of the higher spin algebra corresponding to the spinor singleton. In even dimensions one finds infinitely many deformations of the higher spin algebra labelled by the eigenvalues of Casimir operator of the little group SO(d–2)for massless representations.« less
  • Using an invariant operator in the enveloping algebra of SIM ({ital d}{minus}1,1) (the similitude subgroup of the conformal group in {ital d} dimensions), conformal invariance, and the recent result for the eigenvalue of a generalized helicity'' operator, the eigenvalue of massless fields under scale transformations is computed in higher even dimensions.