The Tate form on steroids: resolution and higher codimension fibers
The Tate form on steroids: resolution and higher codimension fibers
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类固醇的泰特形式：分辨率和更高的余维纤维
DOI：
10.1007/jhep04(2013)061
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发表时间：
2013
影响因子：
5.4
通讯作者：
Lawrie C
中科院分区：
文献类型：
--
作者：
Lawrie C
奇异椭圆纤维Calabi-Yau四折的f理论为从几何角度研究包括物质和汤川耦合在内的四维超对称规范理论提供了一个环境。规范自由度产生于余维数为1的奇异位点，物质和汤川耦合产生于更高余维数的增强奇异点处。构造了余维为ADE型奇异的椭圆型Calabi-Yau四重的奇异Tate形式的解析，并研究了余维为2和3的纤维的结构。我们确定了沿最小奇异座一般为Kodaira型的高协维纤维，从而与低能量规理论直觉相一致。此外，我们提供了高余维纤维的补充描述，这也将适用于非极小奇点。协维数为2的纤维中不可约分量对应于ADE量规组表示的权值。它们可以在余维3中进一步分裂，这与汤川耦合的产生是一致的。应用这一推理，我们然后大胆地研究非极小奇点，它出现在沿余维3的A型，以及在余维2的D和E型。在这种情况下，纤维是非kodaira的，然而，通过考虑沿更高余维的纤维组分的分裂，可以获得对这些奇点的一些见解，这些奇点显示出与相应规范组的物质和汤川耦合一致。
F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensionalsupersymmetric gauge theories, includingmatter and Yukawa couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with an ADE type singularity in codimension 1 and study the structure of the fibers in codimension 2 and 3. We determine the fibers in higher codimension which in general are of Kodaira type along minimal singular loci, and are thus consistent with the low energy gauge-theoretic intuition. Furthermore, we provide a complementary description of the fibers in higher codimension, which will also be applicable to non-minimal singularities. The irreducible components in the fiber in codimension 2 correspond to weights of representations of the ADE gauge group. These can split further in codimension 3 in a way that is consistent with the generation of Yukawa couplings. Applying this reasoning, we then venture out to study non-minimal singularities, which occur for A type along codimension 3, and for D and E also in codimension 2. The fibers in this case are non-Kodaira, however some insight into these singularities can be gained by considering the splitting of fiber components along higher codimension, which are shown to be consistent with matter and Yukawa couplings for the corresponding gauge groups.
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