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Casimir energy for de Sitter branes in bulk AdS\(_5\). (English) Zbl 0997.81090

Summary: The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related to a metric similar in form to the Einstein universe (\(S^4\times R)\). Employing \(\zeta\)-function regularisation we evaluate the one-loop effective potential and show that the vacuum energy is zero for the one brane and non-zero for the two brane configuration. We comment on the back-reaction of this Casimir energy and on the inclusion of a mass term or non-conformal coupling.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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