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

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

Marc Henneaux
(
- CECS, Valdivia and
- Brussels U., PTM
)
,
Cristian Martinez
(
- CECS, Valdivia
)
,
Ricardo Troncoso
(
- CECS, Valdivia
)
,
Jorge Zanelli
(
- CECS, Valdivia
)

Mar, 2006

35 pages

Published in:

Annals Phys. 322 (2007) 824-848

e-Print:

hep-th/0603185 [hep-th]

DOI:

10.1016/j.aop.2006.05.002

Report number:

CECS-PHY-06-04,
NSF-KITP-06-20,
ULB-TH-06-05

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Abstract:

We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in

D\geq 4

dimensions when the mass of the scalar field is in the range

m_{\ast}^{2}\leq m^{2}<m_{\ast} ^{2}+l^{-2}

. Here,

l

is the AdS radius, and

m_{\ast}^{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).

Note:

37 pages, no figures, plain latex. Typos corrected, comments and references added Report-no: CECS-PHY-06/04, NSF-KITP-06-20, ULB-TH/06-05

gravitation: anti-de Sitter
field theory: scalar
higher-dimensional
coupling: minimal
mass dependence
Hamiltonian formalism
asymptotic behavior

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Figures(0)

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