A three‐generation Calabi‐Yau manifold with small Hodge numbers
A three‐generation Calabi‐Yau manifold with small Hodge numbers
复制标题
具有小Hodge数的三代Calabi-Yau流形
DOI：
10.1002/prop.200900106
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Rhys Davies
中科院分区：
文献类型：
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作者：
Volker Braun;P. Candelas;Rhys Davies
给出了具有欧拉数- 72且允许两组12阶自同构自由作用的完全交Calabi‐Yau流形Y。这两个群是循环群s12i和非阿贝尔双环群s12i。商流形有χ =‐6和Hodge数(h11, h21) =(1,4)。在规范群中标准嵌入自旋连接，Y得到具有3代手性粒子的E6规范理论。细谷机制结合背景规场的连续变形，可能进一步破坏规组。对于非阿贝尔商，我们得到了一个具有3代的模型，其中规范群被分解为标准模型。此外，商群发育3个折叠点是有限制的。这些奇异点可以同时得到另一个流形(h11, h21) =(2,2)，它正好位于Calabi‐Yau流形分布的顶端。这强烈地表明，这个流形在商Y上的3代模型中存在异质真空。流形Y也可以被实现为环面变体中的超曲面。对称群不具有历史意义，但我们可以通过改编Batyrev的构造来识别商流形的镜像。
We present a complete intersection Calabi‐Yau manifold Y that has Euler number ‐72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group ℤ12 and the non‐Abelian dicyclic group Dic3. The quotient manifolds have χ = ‐6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the non‐Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi‐Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in a toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.