# Error in Wikipedia on a flipped $SO(10)$ model

In the description of Wikipedia of flipped SO(10) model, it says that:

1. In flipped $$SO(10)$$ models, however, the gauge group is $$[SO(10)_F × U(1)_B]/Z_4$$.

2. If we suppose $$[SU (5) × U(1)_χ ]/ Z_5$$ is a subgroup of $$SO(10)_F$$, then we have the intermediate scale symmetry breaking $$[SO(10)_F × U(1)_B]/Z_5 → [ SU(5) × U(1)_χ]/Z_5$$ where $$\chi=-{A\over 4}+{5B\over 4}$$.

My question is that

• should $$[SO(10)_F × U(1)_B]/Z_4$$ and $$[SO(10)_F × U(1)_B]/Z_5$$ mentioned above, they are the same group or not? Is that one of them has a typo and indeed are the same as $$[SO(10)_F × U(1)_B]/Z_4$$?

• What exactly are the $$A$$ and $$B$$ in $$\chi=-{A\over 4}+{5B\over 4}$$? I think that $$B$$ stands for a $$U(1)$$, and $$B$$ does not imply baryon, correct? But $$A$$ does not show up anywhere on the Wikipedia page.

• $SO(10)$ does not even have a normal $Z_5$ subgroup so the second option makes little sense. Mar 7, 2021 at 22:59

1. Wiki "In flipped $$SO(10)$$ models, however, the gauge group is not just $$SO(10)$$ but $$SO(10)_F \times U(1)_B$$ or $$[SO(10)_F \times U(1)_B]/\mathbf Z_4$$." $$\to$$

My suggestion on the correction to a gauge group $$Spin(10)$$ but $$Spin(10)_F \times U(1)_B$$ or $$[Spin(10)_F \times U(1)_B]/\mathbf Z_4$$. This is because the $$Spin(10)$$ has a $$\mathbf Z_4$$ center.

1. Wiki "If we suppose $$[SU(5) \times U(1)_A]/\mathbf Z_5$$ is a subgroup of $$SO(10)_F$$, then we have the intermediate scale symmetry breaking $$[SO(10)_F \times U(1)_B]/\mathbf Z_4 \to [SU(5) \times U(1)_\chi]/\mathbf Z_5$$"

This statement seems wrong. My suggestion on the correction to

$$U(5) = [SU(5) \times U(1)_A]/\mathbf Z_5$$ or $$U(5)' = [SU(5) \times U(1)_\chi]/\mathbf Z_5$$. $$U(5)$$ is a subgroup of $$SO(10)$$. But $$U(5)$$ is not a subgroup of $$Spin(10)$$. Because we cannot lift the inclusion of $$U(5)$$ to $$SO(10)$$ to its double cover $$Spin(10)$$. So we cannot have $$[SU(5) × U(1)_A]/\mathbf Z_5$$ as a subgroup of $$Spin(10)_F$$. I think that $$[Spin(10)_F × U(1)_B]/\mathbf Z_4$$ does not contain U(5) = $$[SU(5) \times U(1)_A]/\mathbf Z_5$$ nor contain $$U(5)' = [SU(5) \times U(1)_\chi]/\mathbf Z_5$$ either as a subgroup. So the whole thing there does not work in this part.

Maybe other experts can comment.

• I did not give a complete understanding. There are some gaps. It will be nice someone can make comments about these... Aug 15, 2021 at 20:30
• thanks so much + 1, I will be glad if you or someone can clarify more Aug 17, 2021 at 13:27