Modification of Predictions of Grand Unified Theories in the Presence of Spontaneous Compactification

There are speculations that grand unified theories (GUT's) may arise from higher-dimensional models of gravity in which the extra dimensions are spontaneously compactified. The GUT predictions for proton decay and sin²θw can be significantly modified when nonrenormalizable interactions, scaled by inverse powers of the compactification scale Mc, are added to the standard GUT Lagrangian. For example, the decay rate for p→e⁺π⁰ in minimal SU(5) can be lowered by one (two) orders of magnitude if Mc is on the order of 10¹⁷ GeV. However, sin²θw then decreases by 0.005 (0.01). The SO(10) model is also discussed.