Geometric bounds on Kaluza–Klein masses

Abstract

We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza-Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favoured for phenomenological purposes.

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“…It is also known that, for m ≥ 2, there exist upper bounds to the eigenvalues µ n (counted with multiplicity, 0 = µ 0 (Σ) < µ 1 (Σ) ≦ µ 2 (Σ) ≦ · · ·) [29] (there is an incorrect sign in [32])…”

“…As for m-dimensional compact hyperbolic manifolds, there are a number of estimates of µ 1 (= √ E 1 ) in the mathematical literature, see, e.g., [29]. If the Ricci curvature R( ) is bounded below by −(m − 1)/ l 2 , then µ It is also known that, for m 2, there exist upper bounds to the eigenvalues µ n (counted with multiplicity, 0 = µ 0 ( ) < µ 1 ( ) µ 2 ( ) • • •) [29] (there is an incorrect sign in [32]) (m = odd).…”