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

Journal Article · Sun Apr 15 04:00:00 EDT 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.05.002· OSTI ID:20976745

Henneaux, Marc ^[1]; Martinez, Cristian ^[1]; Troncoso, Ricardo ^[1]; Zanelli, Jorge ^[1]

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1. Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)

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)

• OSTI ID: 20976745
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 4 Vol. 322; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ANTI DE SITTER GROUP
ANTI DE SITTER SPACE
BOUNDARY CONDITIONS
GRAVITATION
HAMILTONIANS
MASS
SCALAR FIELDS