We study the moduli spaces of heterotic/type II dual pairs in four dimensions with N=2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non-perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in $α'$.
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincaré polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.
Moduli Dependent mu-Terms in a Heterotic Standard Model
本文提出了一种计算杂种标准模型中非零Higgs μ项的形式。这是通过计算与向量丛模（phi），希格斯（H）和希格斯共轭（Hbar）超场相关的上同调群的立方积来实现的。这导致在低能量超势中与φ H Hbar成比例的项，对于非零模量期望值，产生形式为H Hbar的模量相关的μ项<phi>。据发现，这些相互作用受到两个非常严格的选择规则，每一个所产生的勒雷谱序列，这大大减少了模的数量，可以耦合到希格斯-希格斯共轭场。我们应用我们的形式主义一个特定的杂种优势标准模型真空。在这种情况下，非零立方相互作用φ H Hbar明确计算，并显示只包含十九个向量束模中的四个。
Complex structure moduli of a Calabi-Yau threefold in $N=1$ supersymmetric heterotic compactifications can be stabilized by holomorphic vector bundles. The stabilized moduli are determined by a computation of Atiyah class. In this paper, we study how this mechanism work in the context of elliptically fibered Calabi-Yau manifolds where complex structure moduli space contains two kinds of moduli, ones from base and ones from fibration. With spectral cover bundles, we find three types of situations when holomorphicity of bundles is determined by algebraic cycles supported on special choice of com…
This paper discusses the dilaton, Kähler moduli and hidden sector matter chiral superfields of heterotic $M$-theory vacua in which the hidden sector gauge bundle is chosen to be a line bundle with an anomalous U(1) structure group. For simplicity of notation, the theory is compactified on a Calabi-Yau threefold with $h^{1,1}=1$, although all methods and results apply to more general heterotic compactifications. After introducing a non-perturbative $F$-term potential and coupling to supergravity, the canonically normalized scalar and fermion mass eigenstates, evaluated around a fixed supersymme…
Compactifications of the heterotic string on T^d are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)^{d+16} left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups. We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not. For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II_{1,17}. More general algorithms to explore the moduli space ar…
Heterotic-Type II duality in the hypermultiplet sector
我们重新讨论了在K3 x T^2上紧化的杂化弦论与在超多重态扇区中的卡-丘三重X上紧化的IIA型弦论之间的对偶性。在经典有效作用量的水平上，我们导出了相应模空间的场变量之间的显式映射。我们确定的参数化的K3模空间符合Ferrara-Sabharwal形式。从全纯预势的表达式中，我们猜想X和它的镜像都必须是K3纤维化，以使IIA型理论具有杂种对偶。然后，我们专注于该区域的模空间的度量表示在一个prepotential双方的对偶。应用对偶性，我们导出了一个规范丛的杂化超多重态度规，它被简化为24个点状瞬子。利用T^3上的杂种优势理论和K3上的M-理论之间的对偶性证实了这一结果。最后研究了K3上SU（2）丛的模空间上的超Kaehler度量。
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.
We derive a map relating the gauge symmetry groups of heterotic strings on $T^4$ to other components of the moduli space with rank reduction. This generalizes the results for $T^2$ and $T^3$ which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat $G$-bundles over $T^2$ with $G$ non-simply-connected. These res…
