We discuss family unification in grand unified theory (GUT) based on an |$SU(19)$| GUT gauge group broken to its subgroups, including a special subgroup. In the |$SU(19)$| GUT on the six-dimensional (6D) orbifold space |$M^4imes T^2/mathbb{Z}_2$|?, three generations of the 4D Standard Model Weyl fermions can be embedded into 6D bulk Weyl fermions in an |$SU(19)$| second-rank anti-symmetric tensor representation. 6D and 4D gauge anomalies can be canceled out by considering proper matter content without 4D exotic chiral fermions at low energies.
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机译：我们基于| $ SU（19）$ |讨论大统一理论（GUT）中的家庭统一。 GUT量规组分为其子组，包括一个特殊的子组。在| $ SU（19）$ |中在六维（6D）双倍空间| $ M ^ 4 x T ^ 2 / mathbb {Z} _2 $ |？上的GUT上，可以将三代4D标准模型Weyl费米子嵌入到6D本体Weyl费米子中一个| $ SU（19）$ |二阶反对称张量表示。可以通过考虑适当的物质含量来消除6D和4D规范异常，而无需使用低能量的4D外来手性费米子。
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