Anomalies of Discrete Symmetries and Gauge Coupling Unification
Anomalies of Discrete Symmetries and Gauge Coupling Unification
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离散对称异常与规范耦合统一
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发表时间：
2006
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通讯作者：
T. Araki
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作者：
T. Araki
将离散对称的异常定义为路径积分测度的雅可比矩阵。假设低能的异常在基本尺度上被格林-施瓦茨机制抵消，我们研究了异常离散族对称的可能的Kac-Moody能级。作为第一个例子，我们考虑了具有跷跷板机制的最小超对称标准模型中的离散阿贝尔重子数和轻子数对称，我们发现规范耦合的普通统一与GS条件不一致，这表明希格斯双重态可能存在。我们考虑了最近提出的各种具有非阿贝尔离散族对称的超对称模型。在具有$Q_{6}$族对称的超对称例子中，GS条件使得规范耦合统一接近普朗克尺度。
The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example, we consider discrete abelian baryon number and lepton number symmetries in the minimal supersymmetric standard model with the see-saw mechanism, and we find that the ordinary unification of gauge couplings is inconsistent with the GS conditions, indicating the possible existence of further Higgs doublets. We consider various recently proposed supersymmetric models with a non-abelian discrete family symmetry. In a supersymmetric example with $Q_{6}$ family symmetry, the GS conditions are such that the gauge coupling unification appears close to the Planck scale.