Shape versus Volume: Making Large Flat Extra Dimensions Invisible

Abstract

Much recent attention has focused on theories with large extra compactified dimensions. However, while the phenomenological implications of the volume moduli associated with such compactifications are well understood, relatively little attention has been devoted to the shape moduli. In this paper, we show that the shape moduli have a dramatic effect on the corresponding Kaluza-Klein spectra: they change the mass gap, induce level crossings, and can even be used to interpolate between theories with different numbers of compactified dimensions. Furthermore, we show that in certain cases it is possible to maintain the ratio between the higher-dimensional and four-dimensional Planck scales while simultaneously increasing the Kaluza-Klein graviton mass gap by an arbitrarily large factor. This mechanism can therefore be used to alleviate (or perhaps even eliminate) many of the experimental bounds on theories with large extra spacetime dimensions.