Computing the grand-unification mass in terms of the lengths of the fifth or sixth dimension

Abstract

N = 2 supersymmetric GUTs can be formulated in a five-or six-dimensional spacetime. The grand unification mass m X can be computed in terms of the lengths of the extra compact dimensions: in the simplest case we find m X = (10π h ̵ /3L 5(6)c)n , where n is a fixed integer (or possibly a half-integer). The masses of the electroweak gauge bosons W± and Z are already present in the five- or six-dimensional theory, while the masses of the very heavy grand-unification bosons ( X ± 4 3 , Y ± 1 3 , … ) mostly originate from the large momenta they carry along the compact fifth or sixth dimension.