Codimension-3 Singularities and Yukawa Couplings in F-theory
Codimension-3 Singularities and Yukawa Couplings in F-theory
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DOI：
10.1016/j.nuclphysb.2009.07.021
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发表时间：
2009-01
期刊：
影响因子：
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通讯作者：
Hirotaka Hayashi;T. Kawano;R. Tǎtar;T. Watari
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文献类型：
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作者：
Hirotaka Hayashi;T. Kawano;R. Tǎtar;T. Watari
f理论是大统一理论中所有汤川耦合产生并使其计算成为可能的框架之一。带电物质多重态的汤川耦合假定是在基复三叠的余维-3奇点周围产生的，最近的研究已经证实了这种耦合适用于最简单的余维-3奇点。然而，f理论紧化的几何要复杂得多。对于一般的f -理论紧化，诸如余维-3奇点周围的通量组态、局部几何的场论公式和零模波函数的行为等问题实际上从未被解决过。我们将在本文中讨论所有这些问题，并进一步讨论在这些奇点处产生的汤川耦合的性质。然而，为了计算低能有效理论的汤川耦合，必须将复杂曲面上波函数的局部描述和复杂曲线上零模的全局表征结合在一起。我们通过重新考察f理论紧化中手性带电物质的特征，发现了它们之间的关系。f理论中光谱曲面的内在定义是关键概念。作为双积，我们发现了一种新的理解异质- f理论对偶的方法，提高了现有的与余维-3奇点相关的对偶映射的精度。
F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic–F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.