Wightman function and vacuum fluctuations in higher dimensional brane models
- Department of Physics, Yerevan State University, 1 Alex Manoogian Street, 375049 Yerevan (Armenia) and Abdus Salam International Centre for Theoretical Physics, 34014 Trieste (Italy)
The Wightman function and the vacuum expectation value of the field square are evaluated for a massive scalar field with a general curvature coupling parameter subject to Robin boundary conditions on two codimension-one parallel branes located on a (D+1)-dimensional background spacetime AdS{sub D{sub 1}}{sub +1}x{sigma} with a warped internal space {sigma}. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to manifestly extract the part due to the bulk without boundaries. Unlike the purely anti-de Sitter (AdS) bulk, the vacuum expectation value of the field square induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The brane induced part in this expectation value vanishes when the brane position tends to the AdS horizon or the AdS boundary. The asymptotic behavior of the vacuum densities near the branes and at large distances is investigated. The contribution of Kaluza-Klein modes along {sigma} is discussed in various limiting cases. In the limit when the curvature radius for the AdS spacetime tends to infinity, we derive the results for two parallel Robin plates on the background spacetime R{sup (D{sub 1},1)}x{sigma}. For strong gravitational fields corresponding to large values of the AdS energy scale, both the single brane and interference parts of the expectation values integrated over the internal space are exponentially suppressed. As an example the case {sigma}=S{sup 1} is considered, corresponding to the AdS{sub D+1} bulk with one compactified dimension. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed.
- OSTI ID:
- 20776750
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevD.73.044012; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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