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We compute the one-loop Casimir energy of gravity and matter fields, obeying various boundary conditions, in 5-dimensional S^1/Z_2 and 6-dimensional T^2/Z_k orbifolds. We discuss the role of the Casimir energy in possible radius stabilization mechanisms and show that the presence of massive as well as massless fields can lead to minima with zero cosmological constant. In the 5-d orbifold, we also consider the case where kinetic terms localized at the fixed points are not small. We take into account their contribution to the Casimir energy and show that localized kinetic terms can also provide a mechanism for radius stabilization. We apply our results to a recently proposed 5-dimensional supersymmetric model of electroweak symmetry breaking and show that the Casimir energy with the minimal matter content is repulsive. Stabilizing the radius with zero cosmological constant requires, in this context, adding positive bulk cosmological constant and negative brane-tension counterterms.
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Recently Randjbar-Daemi and Shaposhnikov put forward a 4-dimensional effective QED coming from a Nielsen-Olesen vortex solution of the abelian Higgs model with fermions coupled to gravity in D=6. However, exploring possible physical consequences of such an effective QED was left open. In this letter we study the corresponding effective Casimir effect. We find that the extra dimensions yield fifth and third inverse powers in the separation between plates for the modified Casimir force which are in conflict with known experiments, thus reducing the phenomenological viability of the model.
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Flavor symmetry has been widely studied for figuring out the masses and mixing angles of standard-model fermions. In this paper we present a framework for handling flavor symmetry breaking where the symmetry breaking is triggered by boundary conditions of scalar fields in extra-dimensional space. The alignment of scalar expectation values is achieved without referring to any details of scalar potential and its minimization procedure. As applications to non-abelian discrete flavor symmetries, illustrative lepton mass models are constructed where the S3 and A4 flavor symmetries are broken down to the directions leading to the tri-bimaximal form of lepton mixing and realistic mass patterns.
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