Radius stabilization and anomaly-mediated supersymmetry breaking

We analyze in detail a specific 5-dimensional realization of a “brane-universe” scenario where the visible and hidden sectors are localized on spatially separated 3-branes coupled only by supergravity, with supersymmetry breaking originating in the hidden sector. Although general power counting allows order ${1/M}_{\mathrm{Planck}}^2$ contact terms between the two sectors in the 4-dimensional theory from exchange of supergravity Kaluza-Klein modes, we show that they are not present by carefully matching to the 5-dimensional theory. We also find that the radius modulus corresponding to the size of the compactified dimension must be stabilized by additional dynamics in order to avoid runaway behavior after supersymmetry breaking and to understand the communication of supersymmetry breaking. We stabilize the radius by adding two pure Yang-Mills sectors, one in the bulk and the other localized on a brane. Gaugino condensation in the 4-dimensional effective theory generates a superpotential that can naturally fix the radius at a sufficiently large value that supersymmetry breaking is communicated dominantly by the recently discovered mechanism of anomaly mediation. The mass of the radius modulus is large compared to $m_{3/2}.$ The stabilization mechanism requires only parameters of order one at the fundamental scale, with no fine-tuning except for the cosmological constant.