Shadows of the Planck scale: Scale dependence of compactication geometry

By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant shadows over low-energy physics. These shadows distort our perceptions of the compactification geometry associated with large extra dimensions and place a fundamental limit on our ability to probe the geometry of compactification by measuring Kaluza-Klein states. We also find that compactification geometry is effectively renormalized as a function of energy scale, with renormalization group equations describing the flow of geometric parameters such as compactification radii and shape angles as functions of energy.