6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
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DOI：
10.1016/j.nuclphysb.2017.06.024
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Y. Fujimoto;K. Hasegawa;Kenji Nishiwaki;M. Sakamoto;Kentaro Tatsumi
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文献类型：
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作者：
Y. Fujimoto;K. Hasegawa;Kenji Nishiwaki;M. Sakamoto;Kentaro Tatsumi
在保持四维洛伦兹结构的条件下，我们对矩形上的6维狄拉克费米子Ψ的可能边界条件进行了分类，并推导了在两种特定边界条件下(i) 4维手性正分量在边界处为零和（ii）内手性正分量在边界处为零的零模和非零KK模的轮廓和谱。在(i)的情况下，出现了两个简并的手性零模，它们被一个角参数θ指向矩形的特定方向。这就暗示了在标准模型的物质场中追求三代起源的新方向，即使在六维中没有实现三次简并零模。当这些6d费米子与具有真空期望值的6d标量偶联时，θ构成由汤川相互作用组成的零模费米子质量矩阵。角参数θ的出现源于在矩形额外维度上的退化手性零模式的旋转对称性，因为它们没有边界。在（ii）的情况下，虽然没有出现手性无质量零模，但这种旋转对称被提升为二维共形对称。我们还详细讨论了矩形模型与轨道模型的对应关系。
We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i) 4d-chirality positive components being zero at the boundaries and (ii) internal chirality positive components being zero at the boundaries. In the case of (i), twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameterθ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value,θcontributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameterθoriginates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii), this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.