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When closed strings propagate in extra compactified dimensions, a richspectrum of Kaluza-Klein states and winding states emerges. Since the masses ofKaluza-Klein states and winding states play a reciprocal role, it is oftenbelieved that either the lightest Kaluza-Klein states or the lightest windingstates must be at or below the string scale. In this paper, we demonstrate thatthis conclusion is no longer true for compactifications with non-trivial shapemoduli. Specifically, we demonstrate that toroidal compactifications exist forwhich all Kaluza-Klein states as well as all winding states are heavier thanthe string scale. This observation could have important phenomenologicalimplications for theories with reduced string scales, suggesting that it ispossible to cross the string scale without detecting any states associated withspacetime compactification.Comment: 8 pages, LaTeX, no figure

Kaluza-Klein States versus Winding States: Can Both Be above the String Scale?