Computing Yukawa couplings from magnetized extra dimensions
Computing Yukawa couplings from magnetized extra dimensions
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从磁化额外维度计算汤川耦合
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
F. Marchesano
中科院分区：
文献类型：
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作者：
D. Cremades;L. Ibáñez;L. Ibáñez;F. Marchesano
我们计算了涉及磁通量的高维超杨米尔斯理论环形致密化中的手性物质场的汤川耦合。具体来说，我们关注 D=10 超杨米尔斯理论的环形紧致化，它可以作为 I 型、II 型或异质弦的低能极限来获得。手性是通过在每个 2 环中打开恒定磁通量来获得的。我们的结果是一般性的，也可以应用于较低的 D = 6,8 维场论。我们求解狄拉克和拉普拉斯方程以找出额外维度中波函数的显式形式。汤川耦合被计算为两个外尔费米子和一个复标量在紧凑维度上的重叠积分。在 IIB 型（或 I 型）弦理论的情况下，模型是 T-对偶（定向折叠）IIA 型，具有以角度相交的 D6 膜。这些理论可能具有现象学相关性，因为最近构建了 SM 群和三个夸克-轻子代的特定模型。我们发现如此获得的汤川耦合是由黎曼ϑ函数描述的，该函数取决于复杂的结构和威尔逊线背景。根据这些背景的值，汤川纹理的不同图案是可能的。我们讨论了这些结果与相交 D6 膜模型中的类似计算的匹配。在后一种情况下需要字符串计算，而在我们的情况下只需要场论。
We compute Yukawa couplings involving chiral matter fields in toroidal com- pactifications of higher dimensional super-Yang-Mills theory with magnetic fluxes. Specif- ically we focus on toroidal compactifications of D=10 super-Yang-Mills theory, which may be obtained as the low-energy limit of Type I, Type II or Heterotic strings. Chirality is ob- tained by turning on constant magnetic fluxes in each of the 2-tori. Our results are general and may as well be applied to lower D = 6,8 dimensional field theories. We solve Dirac and Laplace equations to find out the explicit form of wavefunctions in extra dimensions. The Yukawa couplings are computed as overlap integrals of two Weyl fermions and one complex scalar over the compact dimensions. In the case of Type IIB (or Type I) string theories, the models are T-dual to (orientifolded) Type IIA with D6-branes intersecting at angles. These theories may have phenomenological relevance since particular models with SM group and three quark-lepton generations have been recently constructed. We find that the Yukawa couplings so obtained are described by Riemann ϑ-functions, which depend on the complex structure and Wilson line backgrounds. Different patterns of Yukawa textures are possible depending on the values of these backgrounds. We discuss the matching of these results with the analogous computation in models with intersecting D6-branes. Whereas in the latter case a string computation is required, in our case only field theory is needed.