A recently constructed limit of K3 has a long neck consisting of segments, each of which is a nilfold fibred over a line, that are joined together with Kaluza-Klein monopoles. The neck is capped at either end by a Tian-Yau space, which is non-compact, hyperkahler and asymptotic to a nilfold fibred over a line. We show that the type IIA string on this degeneration of K3 is dual to the type I$'$ string, with the Kaluza-Klein monopoles dual to the D8-branes and the Tian-Yau spaces providing a geometric dual to the O8 orientifold planes. At strong coupling, each O8-plane can emit a D8-brane to give an O8$^*$ plane, so that there can be up to 18 D8-branes in the type I$'$ string. In the IIA dual, this phenomenon occurs at weak coupling and there can be up to 18 Kaluza-Klein monopoles in the dual geometry. We consider further duals in which the Kaluza-Klein monopoles are dualised to NS5-branes or exotic branes. A 3-torus with $H$-flux can be realised in string theory as an NS5-brane wrapped on $T^3$, with the 3-torus fibred over a line. T-dualising gives a 4-dimensional hyperkahler manifold which is a nilfold fibred over a line, which can be viewed as a Kaluza-Klein monopole wrapped on $T^2$. Further T-dualities then give non-geometric spaces fibred over a line and can be regarded as wrapped exotic branes. These are all domain wall configurations, dual to the D8-brane. Type I$'$ string theory is the natural home for D8-branes, and we dualise this to find string theory homes for each of these branes. The Kaluza-Klein monopoles arise in the IIA string on the degenerate K3. T-duals of this give exotic branes on non-geometric spaces.
We present explicit examples of supergravity solutions corresponding to backreacting localised (non-intersecting) O6 planes in flux reductions of massive IIA supergravity and address some criticism towards the very existence of such solutions. We verify in detail how the smeared orientifold solution becomes a good approximation to the localised solution in the large volume/weak coupling limit, as expected. We also find an exotic solution where prior to backreaction the internal space has a boundary and when backreaction is included the boundary disappears and the space closes off. The exotic e…
We consider the ${\cal N}=1$ superpotential generated in type-II orientifold models by non-geometric fluxes. In particular, we focus on the family of $P$ fluxes, that are related by T-duality transformations to the S-dual of the $Q$ flux. We determine the general rule that transforms a given flux in this family under a single T-duality transformation. This rule allows to derive a complete expression for the superpotential for both the IIA and the IIB theory for the particular case of a $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ orientifold. We then consider how these fluxes modify the generalis…
We extend the $P$-flux analysis carried out recently on the $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ type-II orientifold model to include all the possible non-geometric fluxes. By deriving universal T-duality rules for all the fluxes, we are able to write down a complete expression for the superpotential for both the IIB and IIA theories. By exploiting the universal T-duality rules that apply to all the branes in string theory, we then identify all the exotic branes that can be consistently included to cancel the tadpoles induced by the fluxes. Finally, we derive the representations of these …
Chiral Four-Dimensional N=1 Supersymmetric Type IIA Orientifolds from Intersecting D6-Branes
我们在T^6/（Z_2 x Z_2）上构造了N=1个超对称的IIA型四维定向折叠，其中D 6-膜相交成角。在模型中使用不完全与O 6平面对齐的D 6-膜，可以构建许多具有手征物质的超对称模型，包括那些具有标准模型和大统一规范群的模型。我们寻找了真实的规范扇区，并构造了第一个具有SU（3）_C x SU（2）_L x U（1）_Y规范群和三个夸克轻子族的超对称II型定向折叠的例子.除了超对称标准模型的内容，该模型还包含右手中微子，一组（手征但无异常）奇异多重态，以及各种矢量样多重态。一般类的这些建设是相关的熟悉的II型orientifolds的小瞬子转换，在某些情况下，改变的代数，在特定的模型中讨论。这些结构是超对称的，只有特殊选择的无扭模量。我们简要地讨论了超对称性破缺效应远离这一点。这一类超对称定向褶皱模型的M理论提升应该对应于纯粹的几何背景，允许奇异的G_2完整度规，并导致具有手征费米子的四维M理论真空。
我们重新讨论了在T^6/（Z2 x Z2）上构造IIA型定向折叠的问题，它允许（非）-可因子分解格。更具体地说，我们考虑一个具有挠率的（Z2 x Z2 '）定向折叠，其中D 6-膜包裹刚性3-圈。在紧化格是不可因式分解格的情况下，我们得到了模型的建立规则和相容性条件。我们表明，在这一类的配置，（半）现实的模型与奇数的家庭可以很容易地构建，相比之下，紧化的D 6膜包装非刚性周期。我们还表明，奇数的家庭可以得到的因式分解的情况下，而不需要倾斜环面。我们说明了讨论，提出了三个家庭的Pati-Salam模型，没有手征异国情调的因式分解和非因式分解的环形紧化。
Three-Family Supersymmetric Pati-Salam Flux Models from Rigid D-Branes
College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；School of Physics, Henan Normal University（河南师范大学物理学院）
