SU(5)

The original and most minimal Grand Unified Theory (GUT), based on the special unitary group of 5x5 matrices. It elegantly unifies the strong and electroweak forces by placing the quarks and leptons of a single standard model generation into two representations: the 5̄ and the 10. Its great triumph was the successful prediction of the weak mixing angle. However, it faces severe problems: it predicts an unobserved, rapid proton decay via X and Y bosons, and it requires intricate "doublet-triplet splitting" to explain why the Higgs doublet is light while its color-triplet partners are superheavy. While now considered ruled out by experiment, SU(5) remains the foundational prototype for all GUT model-building, a beautiful but flawed first attempt at a complete unification.