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

Title: Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields

Abstract

We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D>=4 dimensions when the mass of the scalar field is in the range m{sub *}{sup 2}=<m{sup 2}<m{sub *}{sup 2}+l{sup -2}. Here, l is the AdS radius, and m{sub *}{sup 2} is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound)

Authors:
 [1];  [1];  [1];  [1]
  1. Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
Publication Date:
OSTI Identifier:
20976745
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 322; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2006.05.002; PII: S0003-4916(06)00114-X; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ANTI DE SITTER GROUP; ANTI DE SITTER SPACE; BOUNDARY CONDITIONS; GRAVITATION; HAMILTONIANS; MASS; SCALAR FIELDS

Citation Formats

Henneaux, Marc, Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine C.P.231, B-1050 Brussels, Martinez, Cristian, Troncoso, Ricardo, and Zanelli, Jorge. Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields. United States: N. p., 2007. Web. doi:10.1016/j.aop.2006.05.002.
Henneaux, Marc, Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine C.P.231, B-1050 Brussels, Martinez, Cristian, Troncoso, Ricardo, & Zanelli, Jorge. Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields. United States. https://doi.org/10.1016/j.aop.2006.05.002
Henneaux, Marc, Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine C.P.231, B-1050 Brussels, Martinez, Cristian, Troncoso, Ricardo, and Zanelli, Jorge. 2007. "Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields". United States. https://doi.org/10.1016/j.aop.2006.05.002.
@article{osti_20976745,
title = {Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields},
author = {Henneaux, Marc and Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine C.P.231, B-1050 Brussels and Martinez, Cristian and Troncoso, Ricardo and Zanelli, Jorge},
abstractNote = {We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D>=4 dimensions when the mass of the scalar field is in the range m{sub *}{sup 2}=<m{sup 2}<m{sub *}{sup 2}+l{sup -2}. Here, l is the AdS radius, and m{sub *}{sup 2} is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound)},
doi = {10.1016/j.aop.2006.05.002},
url = {https://www.osti.gov/biblio/20976745}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 4,
volume = 322,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}