VEV in a two dimensional subspace without breaking the standard model. Depending on the direction of this linear combination, we can break the symmetry to SU(5)×U(1), the Georgi–Glashow model with a U(1) (diag(1,1,1,1,1,-1,-1,-1,-1,-1)), flipped SU(5) (diag(1,1,1,-1,-1,-1,-1,-1,1,1)), SU(4)×SU(2)×U(1) (diag(0,0,0,1,1,0,0,0,-1,-1)), the minimal left-right model (diag(1,1,1,0,0,-1,-1,-1,0,0)) or SU(3)×SU(2)×U(1)×U(1) for any other nonzero VEV. The choice diag(1,1,1,0,0,-1,-1,-1,0,0) is called the Dimopoulos-Wilczek mechanism aka the "missing VEV mechanism" and it is proportional to B−L. The choice of a 16H and a breaks the gauge group down to the Georgi–Glashow SU(5). The same comment applies to the choice of a 126H and a . It is the combination of BOTH a 45/54 and a 16/ or 126/ which breaks SO(10) down to the Standard Model. The electroweak Higgs and the doublet-triplet splitting problem The electroweak Higgs doublets come from an SO(10) 10H. Unfortunately, this same 10 also contains triplets. The masses of the doublets have to be stabilized at the electroweak scale, which is many orders of magnitude smaller than the GUT scale whereas the triplets have to be really heavy in order to prevent triplet-mediated proton decays. See doublet-triplet splitting problem. Among the solutions for it is the Dimopoulos-Wilczek mechanism, or the choice of diag(1,1,1,0,0,-1,-1,-1,0,0) of <45>. Unfortunately, this is not stable once the 16/ or 126/ sector interacts with the 45 sector. Content Matter The matter representations come in three copies (generations) of the 16 representation. The Yukawa coupling is 10H 16f 16f. This includes a right-handed neutrino. One may either include three copies of singlet representations and a Yukawa coupling (the "double seesaw mechanism"); or else, add the Yukawa interaction or add the nonrenormalizable coupling . See seesaw mechanism. The 16f field branches to [SU(5)×U(1)χ]/Z5 and SU(4) × SU(2)L × SU(2)R as Gauge fields The 45 field branches to [SU(5)×U(1)χ]/Z5 and SU(4) × SU(2)L × SU(2)R as and to the standard model [SU(3)C × SU(2)L × U(1)Y]/Z6 as The four lines are the SU(3)C, SU(2)L, and U(1)B−L bosons; the SU(5) leptoquarks which don't mutate X charge; the Pati-Salam leptoquarks and SU(2)R bosons; and the new SO(10) leptoquarks. (The standard electroweak U(1)Y is a linear combination of the bosons.) Proton decay Note that SO(10) contains both the Georgi–Glashow SU(5) and flipped SU(5). Anomaly free from local and global anomalies It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear