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Grand Unified Theories (GUTs)

Attempt to unify the strong, weak, and electromagnetic forces at high energies, often incorporating supersymmetry and predicting proton decay.
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The statement of the theorem

Consider a gauge group GGUTG_{GUT} that unifies the Standard Model groups GSM=SU(3)C×SU(2)L×U(1)YG_{SM} = SU(3)_C \times SU(2)_L \times U(1)_Y. The running of the coupling constants αi\alpha_i is governed by the beta function βi\beta_i: dαidln⁡(μ)=βi(αi)=12×πbiαi2 \frac{d\alpha_i}{d\ln(\mu)} = \beta_i(\alpha_i) = \frac{1}{2\times \pi} b_i \alpha_i^2 where bib_i are the coefficients. GUT unification requires the couplings to meet at a single point ΛGUT\Lambda_{GUT}: α1(ΛGUT)=α2(ΛGUT)=α3(ΛGUT)=αGUT \alpha_1(\Lambda_{GUT}) = \alpha_2(\Lambda_{GUT}) = \alpha_3(\Lambda_{GUT}) = \alpha_{GUT}