标题： 大统一与普朗克尺度：一个由辐射破缺导致对称性破缺的$\mathit{SO}(10)$示例 显示英文标题

标题： Grand unification and the Planck scale: An $\mathit{SO}(10)$ example of radiative symmetry breaking

摘要： 规范耦合的统一和费米子表示仍然是一个吸引人的提议，用于解释标准模型看似巧合的结构。然而，在低能下实现标准模型，统一对称性群必须通过适当的标量势以正确的方式部分破缺。标量势包含多个耦合，其值决定了全局最小点的剩余对称性。其中一些（并且可能许多）对应的对称性破缺模式与标准模型不兼容，因此不可接受。 在这里，我们开始系统地研究辐射对称性破缺，从而约束标量耦合的有效初始条件，例如，在普朗克尺度上。 我们将这些关于可接受标量势的新约束与规范- Yukawa 部分已知的约束结合起来，形成一个通用蓝图，刻画出任何量子引力基本理论的有效场论参数空间。 我们在一个非超对称的$\mathit{SO}(10)$大统一理论中举例说明了我们的蓝图的约束能力，该理论包含一个$\mathbf{16}_H$维和一个$\mathbf{45}_H$维的标量表示。 我们明确表明，成功实现辐射对称性破缺到正确子群的要求显著限制了基础微观动力学。 非可接受的辐射极小值甚至可以完全排除特定的破缺链：在$\mathit{SO}(10)$示例中，Pati-Salam 破缺链无法实现，因为相应的极小值从未是最深的。 显示英文摘要

摘要： Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible. Here, we initiate a systematic study of radiative symmetry breaking to thereby constrain viable initial conditions for the scalar couplings, for instance, at the Planck scale. We combine these new constraints on an admissible scalar potential with well-known constraints in the gauge-Yukawa sector into a general blueprint that carves out the viable effective-field-theory parameter space of any underlying theory of quantum gravity. We exemplify the constraining power of our blueprint within a non-supersymmetric $\mathit{SO}(10)$ GUT containing a $\mathbf{16}_H$- and a $\mathbf{45}_H$-dimensional scalar representation. We explicitly demonstrate that the requirement of successful radiative symmetry breaking to the correct subgroups significantly constraints the underlying microscopic dynamics. The presence of non-admissible radiative minima can even entirely exclude specific breaking chains: In the $\mathit{SO}(10)$ example, Pati-Salam breaking chains cannot be realised since the respective minima are never the deepest ones.