论文标题
重力耦合$ {\ cal n} = 2 $杂质压缩Wilson Lines
Gravitational couplings in ${\cal N}=2$ heterotic compactifications with Wilson lines
论文作者
论文摘要
在本文中，我们计算$（K3 \ times t^2）/\ Mathbb {z} _n $和$ e_8 \ times e_8 $的杂丝串的重力耦合，并预测了dual calabi yau Yau yau歧管的Gopakumar Vafa不变式。这里$ \ mathbb {z} _n $在与$ m_ {23} $相关的$ k3 $上充当$ k3 $的自动形态，$ s^1 $ of $ t^2 $的$ m_ {23} $和$ 1/n $的偏移。我们详细研究了标准的$ n = 2,3 $和几个非标准嵌入，其中$ k3 $被用作toroidal orbifolds $ t^4/\ mathbb {z} _4 $和$ t^4/\ mathbb {Z} _3 $。从这些计算中，我们在存在单个Wilson线的情况下，在这些Orbifold模型的扰动前攻击前提取多项式项。我们还显示标准嵌入的gopakumar vafa不变性的完整性取决于在$ n <8 $ wilson系列的情况下，扭曲的椭圆属的傅立叶变换的傅立叶系数的完整性。
In this paper we compute the gravitational couplings of the heterotic string compactified on $(K3\times T^2)/\mathbb{Z}_N$ and $E_8\times E_8$ and predict the Gopakumar Vafa invariants of the dual Calabi Yau manifold in presence of Wilson lines. Here $\mathbb{Z}_N$ acts as an automorphism on $K3$ associated with the conjugacy classes of $M_{23}$ and a shift of $1/N$ on one of the $S^1$ of $T^2$. We study in detail the cases $N=2,3$ for standard and several non-standard embeddings where $K3$ is realized as toroidal orbifolds $T^4/\mathbb{Z}_4$ and $T^4/\mathbb{Z}_3$. From these computations we extract the polynomial term in perturbative pre-potential for these orbifold models in presence of a single Wilson line. We also show for standard embeddings the integrality of the Gopakumar Vafa invariants depend on the integrality of Fourier coefficients of Fourier transform of the twisted elliptic genus of $K3$ in presence of $n<8$ Wilson lines.
