我们考虑杂种E8 X E8弦论，它产生了四维类标准模型，并允许它们的SO（10）嵌入。我们研究了两种不同的紧化方案：自由费米子公式和orbifold结构。在自由费米子公式中给出的例子中，我们直接在弦水平上使用自由费米子边界条件，而不是在有效低能场论中，探讨了额外希格斯表象的去除。此外，通过采用标准的分析平坦的方向，我们提出了一个准现实的三代弦模型，其中严格的F-和D-平坦的解决方案似乎不存在的所有订单的超势。我们表明，通过选择一个不可因式分解的紧化格，定义为倾斜其标准的简单的根，我们减少了总的代数。最后，给出了E8 × E8轨道紧化的模不变配分函数的构造。
英文摘要：
We consider the heterotic E8 X E8 string theory, which gives rise to four-dimensional Standard-like Models and allows for their SO(10) embedding. We investigate two different schemes of compactification: the free fermionic formulation and the orbifold construction. In the examples presented in the free fermionic formulation we explore the removal of the extra Higgs representations by using the free fermion boundary conditions directly at the string level, rather than in the effective low energy field theory. Moreover, by employing the standard analysis of flat directions we present a quasi-realistic three generation string model in which stringent F- and D- flat solutions do not appear to exist to all orders in the superpotential. We show that, by choosing a non-factorisable compactification lattice, defined by skewing its standard simple roots, we decrease the total number of generations. Finally, the construction of modular invariant partition functions for E8 X E8 orbifold compactifications is presented.
We consider toroidal asymmetric orbifolds of the heterotic string preserving all 16 supercharges, developing a general formalism to study components of the moduli space characterized by rank reduction of the gauge group. In particular we construct six- and four-dimensional heterotic islands with no massless moduli other than the dilaton. The formalism involves the Leech lattice, its automorphisms and their corresponding invariant and normal, or coinvariant, sublattices.
By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on $T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactified on $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While the heterotic compactification space is straightforward, the description of the gauge bundle is subtle, involving the physics of point-like instantons on orbifold singularities. By comparing the gauge groups of the dual theories, we deduce behavior of a "half-$G_{2}$" limit, which is the M-theory analog of the stable degeneration limit of F-theory. The heterotic backgrounds ex…
Heterotic orbifold models on Lie lattice with discrete torsion
给出了一类新的不可因式分解环面上的ZNxZM杂化轨道折叠，其边界条件由Lie格定义.一般来说，这些轨道褶皱的点群是由Weyl反射和晶格的外自同构生成的。我们分类阿贝尔orbifolds和没有离散挠。然后，我们发现这些模型中的一些模型具有比可因子化环面T^2 x T^2 x T^2上的模型更小的欧拉数。有一种可能性，这些orbifolds提供更小的代数N=1手征物质场比可因子化模型。
Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher's gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non-Lorentz invariant gauge fixing. A left-over of the gauge symmetry can be used to removed the doubled constant zero modes so that D physical target space coordinate remain. This can be thought of as the worldsheet realization of the strong constraint of double field theory. The extension of this description to the heterotic theory is straightforward as all results are written in terms o…
The moduli space of the maximally supersymmetric heterotic string in d-dimensional Minkowski space contains various components characterized by the rank of the gauge symmetries of the vacua they parametrize. We develop an approach for describing in a unified way continuous Wilson lines which parametrize a component of the moduli space, together with discrete deformations responsible for the switch from one component to the other. Applied to a component that contains vacua with SO(2n+1) gauge-symmetry factors, our approach yields a description of all backgrounds of the component in terms of fre…
We study the global structure of vacua of heterotic strings compactified on orbifolds $T^4/Z_N$ (N=2,3) in the presence of heterotic 5-branes. Gauge symmetry breaking associated with orbifold is described by instantons in the field theory. Phase transition between small instantons and heterotic 5-branes provides top-down, stringy account to the spectrum and modular invariance condition. Also it takes us from one vacuum to another by emitting and absorbing instantons. This means that many vacua with different gauge theory are in fact connected and are inherited from perturbative vacua. It follo…
Z_3 orbifolds of the SO(32) heterotic string: 1 Wilson line embeddings
本文研究了具有一条离散Wilson线的6维Z_3轨道上SO（32）杂化弦的紧化。给出了所有可能的嵌入的完整集合，总共159个。SO（32）的不破断子群列表。最近由J. E. Kim [hep-th/0301177]对于半现实的E_8 x E_8杂种弦模型，发生在几个嵌入中，以及在统一弦模型中可能感兴趣的其他组。讨论了额外规范群因子的隐藏程度，并与E_8 × E_8的情况进行了比较。沿着存在有效隐藏扇区的平坦方向，这里描述的嵌入提供了在E_8 x E_8杂种弦中不可能的隐藏规范群。
Voisin-Borcea Manifolds and Heterotic Orbifold Models
研究了具有非平凡线丛的光滑Voisin-Borcea Calabi-Yau三重轨道上的紧化与杂种优势T^6/Z6轨道模型之间的关系.这个轨道可以看作是T^4/Z3 x T^2的Z2商。我们考虑两步分解，其中间步骤为（K3 x T^2）/Z2。这使我们能够识别对应于几何Kaehler和复杂结构模量的无质量扭曲状态。当所有扭曲几何模量的期望值都为非零时，我们给出了两个模型的匹配。我们发现，即使轨道规范群包含SO（10）因子，一个可能的GUT群，higgsing后的子群甚至不包括标准模型规范群。此外，在Higgsing之后，在剩余规范群下的无质量谱是非手征的。
