Hadamard function and the vacuum currents in braneworlds with compact dimensions: Twobrane geometry
Abstract
We evaluate the Hadamard function and the vacuum expectation value of the current density for a charged scalar field in the region between two codimensionone branes on the background of locally antide Sitter (AdS) spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to an AharonovBohmtype effect on the vacuum currents. There exists a range in the space of the Robin coefficients for separate branes where the vacuum state becomes unstable. Compared to the case of the standard AdS bulk, in models with compact dimensions the stability condition imposed on the parameters is less restrictive. The current density has nonzero components along compact dimensions only. These components are decomposed into the branefree and braneinduced contributions. Different representations are provided for the latter that are well suited for the investigation of the nearbrane, nearAdS boundary and nearAdS horizon asymptotics. An important feature, that distinguishes the current density from the expectation values of the field squared and energymomentum tensor, is its finiteness on the branes. In particular, for Dirichlet boundary conditions the current density vanishes on the branes. We show that, depending on the constants in the boundary conditions, the presence of the branes may either increase or decrease the current density compared with that for the branefree geometry. Applications are given to the RandallSundrum 2brane model with extra compact dimensions. In particular, we estimate the effects of the hidden brane on the current density on the visible brane.
 Publication:

Physical Review D
 Pub Date:
 April 2016
 DOI:
 10.1103/PhysRevD.93.084011
 arXiv:
 arXiv:1512.06569
 Bibcode:
 2016PhRvD..93h4011B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 29 pages, 7 figures, PACS numbers: 04.62.+v, 04.50.h, 11.10.Kk, 11.25.w. arXiv admin note: text overlap with arXiv:1508.07255