2012/10/31 by David M. Jacobs, Glenn D. Starkman, Andrew J. Tolley · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane #Brane cosmology #Casimir effect #Classical mechanics #Context (archaeology) #Curvature #Geometry #Isotropy #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Randall–Sundrum model #Scalar (mathematics) #Theoretical physics #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.87.046007
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 87(4) (American Physical Society) · 50 pages, 9 figures. Updated to match the PRD version
openalex publication_date 2013/02/19 · arxiv created 2014/10/19 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Extra dimensions are a common feature of physics beyond the Standard Model. In a braneworld scenario, local physics on the brane can depend strongly on the brane's location within the bulk. Generically, the relevant properties of the bulk manifold for the physics on/of the brane are neither local nor global, but depend on the structure of finite regions of the bulk, even for locally homogeneous and isotropic bulk geometries. In a recent work, we considered various mechanisms (in a braneworld context) to stabilize the location of a brane within bulk spaces of nontrivial topology. In this work, we elaborate on and generalize that work by considering additional bulk and brane dimensionalities as well as different boundary conditions on the bulk scalar field that provides a Casimir force on the brane, providing further insight on this effect. In D=2+1 (D=5+1), we consider both local and global contributions to the effective potential of a 1-brane (4-brane) wrapped around both the two-dimensional hyperbolic horn and the Euclidean cone, which are used as toy models of an extradimensional manifold. We calculate the total energy due to brane tension and elastic energy (extrinsic curvature) as well as that due to the Casimir energy of a bulk scalar satisfying both Dirichlet and Neumann boundary conditions on the brane. In some cases, stable minima of the potential are found that result from the competition of at least two of the contributions. Generically, any one of these effects may be sufficient when the bulk space has less symmetry than the manifolds considered here. We highlight the importance of the Casimir effect for the purpose of brane stabilization.