Shadows of the Planck Scale: The Changing Face of Compactification Geometry

TL;DR

This paper explores how tiny, Planck-scale extra dimensions can significantly influence low-energy physics, complicating the understanding of compactification geometry and introducing a renormalization group perspective on geometric parameters.

Contribution

It introduces the concept that compactification geometry is energy-dependent and develops renormalization group equations for shape moduli and radii.

Findings

Planck-sized extra dimensions affect low-energy physics.

Compactification geometry is effectively renormalized with energy.

Shape moduli influence the perception of extra dimensions.

Abstract

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 can greatly 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 simply by measuring Kaluza-Klein states. We also discuss the interpretation of compactification radii and hierarchies in the context of geometries with non-trivial shape moduli. One of the main results of this paper is 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.