Casimir Energy and Radius Stabilization in Five and Six Dimensional Orbifolds

TL;DR

Pontón and Poppitz analyze one-loop Casimir energies in 5D S^1/Z_2 and 6D T^2/Z_k orbifolds to explore radius stabilization via quantum effects. They compute gravitational and matter contributions for various boundary conditions, address divergences with fixed-point counterterms, and show how massive fields and brane-localized terms can yield a radion potential with zero four-dimensional cosmological constant under suitable tuning. Applying these results to a 5D SUSY electroweak-breaking model, they find the minimal content induces a repulsive Casimir energy requiring a positive bulk cosmological constant and negative brane tensions to realize a zero-CC minimum, while 6D torus compactifications exhibit modular-dependent stabilization tendencies. Overall, the work demonstrates Casimir-driven radius stabilization in orbifold contexts and highlights the need for UV-complete embeddings to fully assess viability.

Abstract

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.