AI 中文总结
研究共轭边界条件在紧致化五维理论中实现马约拉纳费米子的情况，通过直接计算表明KK模可组合成狄拉克旋量，还研究了相关相互作用，构建扩展跷跷板模型，其性质与传统模型不同，新相互作用致轻子数违反，马约拉纳质量项不违反。
AI 中文摘要
本文讨论共轭边界条件（CBC），其作为在紧致化五维理论（$\mathcal M^4\otimes S^1/Z_2$）中实现马约拉纳费米子的一种方式被研究。在跷跷板机制中起关键作用的马约拉纳费米子通过施加CBC作为零模出现。通过直接计算表明，自由理论中或拉格朗日量二次项水平下，非零卡鲁扎-克莱因（KK）模可组合成狄拉克旋量。KK模扇区存在意外U(1)对称性，零模扇区则无。CBC与轴矢U(1)变换的兼容性在KK模对角化中起关键作用。还研究了与CBC和手征轨形投影兼容的相互作用，发现允许CBC费米子与手征轨形费米子之间存在非平凡体相互作用。作为应用，利用边界条件和这种非平凡体相互作用构建了扩展跷跷板模型，该模型与传统扩展跷跷板模型性质不同，新的非平凡相互作用导致轻子数违反，而模型中的马约拉纳质量项不违反轻子数。
英文摘要
In this paper, we discuss the conjugate boundary condition (CBC), which has recently been studied as a way of realizing a Majorana fermion within a compactified five-dimensional theory ($\mathcal M^4\otimes S^1/Z_2$). The Majorana fermion which plays a crucial role in the seesaw scenario arises as a zero mode (lowest mode) by imposing the CBC. Although each nonzero Kaluza-Klein (KK) mode is also naively expected to be described by two Majorana fermions, we show by direct calculation that they can be combined into a Dirac spinor in the free theory or up to the level of the quadratic term in the Lagrangian. This difference comes from the fact that an accidental U(1) symmetry exists in the KK mode sector, though such a symmetry does not appear in the zero mode sector. We also point out that the compatibility between the CBC and the axial U(1) transformation plays a crucial role in the diagonalization of the KK mode. We also investigate interactions compatible with both the CBC and the chiral orbifold projection. We find that a nontrivial bulk interaction between a CBC fermion and a chiral-orbifold fermion is allowed. As an application, we construct an extended seesaw scenario by utilizing both boundary conditions and such nontrivial bulk interactions. The resulting seesaw scenario has a different property in contrast with the conventional extended seesaw scenario; namely, the above new non-trivial interactions cause lepton number violation (LNV), while the Majorana mass term in our model does not violate lepton number.
Comments21 pages, 1 figure
