Abstract
The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to H = SU(3) C × SU(2) L × U(1) R × U(10) B−L . For all solutions, the fermions which are chiral with respect to H form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2) G × U(1) G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2) G × U(1) G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.
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