我们从F理论出发构造了SU（5）和SO（10）模型。打开U（1）通量，我们可以将SU（5）规范对称性破缺到标准模型（SM）规范对称性，并将SO（10）规范对称性破缺到SU（3）_C X SU（2）_L X SU（2）_R X U（1）_{B-L}规范对称性。特别地，所有的SM费米子Yukawa耦合在SM费米子和Higgs曲线的三重交点处保持了增强的U（1）_a × U（1）_b规范或整体对称性。在背景通量存在的情况下，可以产生SM费米子质量和混合。在我们的模型中，双三重态分裂问题可以自然解决。附加的类矢量粒子可以通过瞬子效应或希格斯机制获得重质量，然后在高尺度下解耦。弦尺度下的SM规范耦合由于U（1）通量效应而分裂，可以通过考虑来自额外的类矢量粒子的重阈值修正来解释。此外，在SU（5）模型中，我们得到了底夸克和τ轻子的汤川耦合统一。在SO（10）模型中，对顶夸克和底夸克有Yukawa耦合统一，对τ轻子和τ中微子有Yukawa耦合统一。
英文摘要：
We construct the SU(5) and SO(10) models from F-theory. Turning on the U(1) fluxes, we can break the SU(5) gauge symmetry down to the Standard Model (SM) gauge symmetry, and break the SO(10) gauge symmetry down to the SU(3)_C X SU(2)_L X SU(2)_R X U(1)_{B-L} gauge symmetry. In particular, all the SM fermion Yukawa couplings preserve the enhanced U(1)_a X U(1)_b gauge or global symmetries at the triple intersections of the SM fermion and Higgs curves. And the SM fermion masses and mixings can be generated in the presence of background fluxes. In our models, the doublet-triplet splitting problem can be solved naturally. The additional vector-like particles can obtain heavy masses via the instanton effects or Higgs mechanism and then decouple at the high scale. The SM gauge couplings at the string scale, which are splitted due to the U(1) flux effects, can be explained by considering heavy threshold corrections from the extra vector-like particles. Moreover, in the SU(5) model, we have the Yukawa coupling unification for the bottom quark and tau lepton. In the SO(10) models, we have the Yukawa coupling unification for the top and bottom quarks, and the Yukawa coupling unification for the tau lepton and tau neutrino.
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we co…
We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due t…
In a weak coupling limit the neighborhood of $E_6$ Yukawa points in $SU(5)$ GUT F-theory models is described by a non-resolvable orientifold of the conifold. We explicitly show, first directly in IIB and then via a mirror symmetry argument, that in this limit the $E_6$ Yukawa coupling is better described as coming from the non-perturbative contribution of a euclidean D1-brane wrapping the non-resolvable cycle. We also discuss how the M-theory description interpolates between the weak and strong coupling viewpoints.
Dynamical Generation of Yukawa Couplings in Intersecting D-brane Models
我们提出了一个方案，在IIA型T^6/Z_2 x Z_2定向折叠的超对称相交D膜模型中，获得夸克-轻子质量产生的非平凡Yukawa耦合矩阵。作为一个例子，我们构造了一个明确的模型，其中四代夸克和轻子以及两对无质量的希格斯场都是复合的。在这个模型中，非平凡的Yukawa相互作用是通过“前子”之间的弦水平的高维相互作用和“前子”的禁闭动力学之间的相互作用得到的。
We compute Yukawa couplings in type IIB string theory compactified on a non factorisable six-torus in the presence of D9 branes and fluxes. The setting studied in detail, is obtained by T-dualising an intersecting brane configuration of type IIA theory compactified on a torus generated by the SO(12) root lattice. Particular deformations of such torus are taken into account and provide moduli dependent couplings. Agreement with the type IIA result is found in a non trivial way. The classical type IIB calculation gives also information on a factor accessible only by quantum computations on the t…
We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different geometrical structures and our understanding of the subject has yet to be consolidated in a unified framework. This short note is based upon a talk that was given by one of the authors at the Nankai Symposium on Mathematical Dialogues. Therefore it is aimed at a mathematical audience of mixed academic background.
We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among un…
Yukawa Coupling Structure in Intersecting D-brane Models
研究了具有相交D-膜的IIA型T^6/（Z_2 x Z_2）定向折叠模型中Yukawa耦合矩阵的结构.在传统的模型中，汤川耦合矩阵是很难实现的，在传统的模型中，生成结构是通过因子化的T^6 = T^2 x T^2 x T^2中D膜的多重相交而出现的。我们研究了新类型的风味结构，汤川耦合是动态生成的，并显示这种类型的模型导致汤川耦合矩阵的非平凡结构，这是现实的。
The unification of gauge and top Yukawa couplings is an attractive feature of gauge-Higgs unification models in extra-dimensions. This feature is usually considered difficult to obtain based on simple group theory analyses. We reconsider a minimal toy model including the renormalisation group running at one loop. Our results show that the gauge couplings unify asymptotically at high energies, and that this may result from the presence of an UV fixed point. The Yukawa coupling in our toy model is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be a…
We compute Yukawa couplings in type IIa string theory compactified on a six-torus in the presence of intersecting D6-branes. The six-torus is generated by an SO(12) root lattice. Yukawa couplings are expressed as sums over worldsheet instantons. Our result extends known expressions to a non-factorisable torus. As an aside we also fill in some details for the factorisable torus and non-coprime intersection numbers.
We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are …
We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the $λϕ^4$ and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are gauge dependent and, further, that they can be removed by a non-multiplicative, though local, field redefinition. An analogous analysis is carried out when General Relativity is replaced with Unimodular Gravity. Thus we show that a…
The IKKT model is proposed as a non-perturbative formulation of superstring theory. We propose a Dirac operator on the noncommutative torus,which is consistent with the IKKT model, based on noncommutative geometry. Next, we consider zero-mode equations of the Dirac operator with magnetic fluxes. We find that zero-mode solutions have the chirality and the generation structures similar to the commutative case. Moreover, we compute Yukawa couplings of chiral matter fields.
We study the fixed point structure of the Higgs-Yukawa model, with its scalar being non-minimally coupled to the asymptotically safe gravity, using the functional renormalization group. We have obtained the renormalization group equations for the cosmological and Newton constants, the scalar mass-squared and quartic coupling constant, and the Yukawa and non-minimal coupling constants, taking into account all the scalar, fermion, and graviton loops. We find that switching on the fermionic quantum fluctuations makes the non-minimal coupling constant irrelevant around the Gaussian-matter fixed po…
