AI 中文总结
研究SU(5) GUT希格斯扇区中超越对称性限制的VEV假设下真空的横向稳定性问题，通过导出模式谱及确定参数选择，发现常见驻点构型在不同情况下分别为局部最小值和鞍点，经计算验证相关特性。
AI 中文摘要
扩展希格斯扇区可在大统一理论（GUTs）中实现多阶段破缺链，产生的中间规范相可能与宇宙学缺陷相关。将真空期望值（VEVs）限制在保留选定子群的构型是识别候选驻点的有效方法，而其在该子空间外波动的稳定性是另一个问题。我们在具有伴随24_H和复对称15_H的可重整化SU(5) GUT希格斯扇区中研究此问题，这是受Langacker-Pi单极子消除的特殊子群实现所推动。在标准伴随背景下，保留中间规范群的15_H VEVs形成一个具有独立色和弱块振幅的两块族。门户相互作用可使这些振幅不等而不改变未破缺规范群。两个独立的混合四次不变量在该两块场空间上求值时变得相同，尽管它们对色弱波动的贡献不同。我们导出这些模式的完整谱，并确定两个从下有界的参数选择，它们在两块场空间上诱导相同的势，但在横向方向具有不同的曲率。常见的驻点构型在一种情况下是局部最小值，在另一种情况下是具有六个负物理模式的鞍点。在完整的54维实标量场空间中直接进行海森矩阵计算可重现解析谱，并验证最小值 - 鞍点的区别以及局部稳定的基准真空。
英文摘要
Extended Higgs sectors can realize multistage breaking chains in grand unified theories (GUTs), and the resulting intermediate gauge phases can be relevant to cosmological defects. Restricting vacuum expectation values (VEVs) to configurations that preserve a chosen subgroup is an efficient way to identify candidate stationary points, while their stability against fluctuations outside this subspace is a separate question. We study this question in a renormalizable $SU(5)$ GUT Higgs sector with an adjoint $24_H$ and a complex symmetric $15_H$, motivated by a special-subgroup realization of Langacker-Pi monopole erasure. On the standard adjoint background, the $15_H$ VEVs that preserve the intermediate gauge group form a two-block family with independent color- and weak-block amplitudes. Portal interactions can make these amplitudes unequal without changing the unbroken gauge group. Two independent mixed quartic invariants become identical when evaluated on this two-block field space, although they contribute differently to color-weak fluctuations. We derive the complete spectrum of these modes and identify two bounded-from-below parameter choices that induce the same potential on the two-block field space but have different curvatures in transverse directions. The common stationary configuration is a local minimum in one case and a saddle with six negative physical modes in the other. Direct Hessian calculations in the full 54-dimensional real scalar field space reproduce the analytic spectrum and verify both the minimum-saddle distinction and locally stable benchmark vacua.
