David M. Jacobs, Glenn D. Starkman, Andrew J. Tolley
Extra-dimensional scenarios have become widespread among particle and gravitational theories of physics to address several outstanding problems, including the dark energy or weak hierarchy problems. In general, the topology and geometry of the full spacetime manifold will be non-trivial, even if our ordinary dimensions have the topology of their covering space. Most compact manifolds are inhomogeneous, even if they admit a homogeneous geometry, and it will be physically relevant where in the extra-dimensions one is located. In this letter, we explore the use of the Casimir effect in a braneworld scenario as a dynamical mechanism to determine and stabilize the location of a single brane. This is possible because the zero point energy in bulk quantum fields that satisfy particular brane boundary conditions depends on the brane location. Thus, there is a position-dependent force on the brane. Here we consider the 2-dimensional horn as a toy model of the extra dimensions and calculate the Casimir energy for a bulk scalar satisfying a Dirchlet boundary condition on a brane that wraps around the horn. For brane tensions above a critical value, a stable energy minimum is achieved as a result of the competition between the Casimir energy and the brane tension. We discuss this as an example of physics that is neither local nor global, but regional.
View original:
http://arxiv.org/abs/1205.1528
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