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Lookup NU author(s): Alan Haydn Knapman, Wade Naylor
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We present a calculation of the zeta function and of the functional determinant for a Laplace-type differential operator, corresponding to a scalar field in a higher-dimensional de Sitter brane back-ground, which consists of a higher-dimensional anti de Sitter bulk spacetime bounded by a de Sitter section, representing a brane. Contrary to the existing examples, which all make use of conformal transformations, we evaluate the zeta function working directly with the higher-dimensional wave operator. We also consider a generic mass term and coupling to curvature, generalizing previous results. The massless, conformally coupled case is obtained as a limit of the general result and compared with known calculations. In the limit of large anti de Sitter radius, the zeta determinant for the ball is recovered in perfect agreement with known expressions, providing an interesting check of our result and an alternative way of obtaining the ball determinant © 2004 The American Physical Society.
Author(s): Flachi A, Knapman A, Naylor W, Sasaki M
Publication type: Article
Publication status: Published
Journal: Physical Review D
Year: 2004
Volume: 70
Issue: 12
ISSN (print): 0556-2821
ISSN (electronic):
Publisher: American Physical Society
URL: http://dx.doi.org/10.1103/PhysRevD.70.124011
DOI: 10.1103/PhysRevD.70.124011
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