论文标题
对纤维CY-3褶皱和非亚洲弱重力猜想的状态计数
State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
论文作者
论文摘要
We extend the dictionary between the BPS spectrum of Heterotic strings and the one of F-/M-theory compactifications on $K3$ fibered Calabi-Yau 3-folds to cases with higher rank non-Abelian gauge groups and in particular to dual pairs between Heterotic CHL orbifolds and compactifications on Calabi-Yau 3-folds with a compatible genus one fibration.我们通过重建Noether-Lefschetz发电机，这些形式显示了如何从Calabi-yau几何形状获得新的超对称指数，这些指数是从Calabi-yau几何形状获得的。后一个物体和矢量值晶格雅各比形式之间存在同构，将它们与六维和五维异质弦的椭圆形属和扭曲的椭圆形属相关联。 Meromorormorphic Jacobi形式产生了纤维对称产品希尔伯特方案的精制共同体的尺寸，并使我们能够完善纤维中的BPS指数，从而获得猜想的实际状态计数。使用矢量值晶格雅各比形式的性质，我们还提供了数学证明，证明了在这类纤维类的calabi-yau 3倍上压实的F-/M理论的非亚伯弱重力猜想。
We extend the dictionary between the BPS spectrum of Heterotic strings and the one of F-/M-theory compactifications on $K3$ fibered Calabi-Yau 3-folds to cases with higher rank non-Abelian gauge groups and in particular to dual pairs between Heterotic CHL orbifolds and compactifications on Calabi-Yau 3-folds with a compatible genus one fibration. We show how to obtain the new supersymmetric index purely from the Calabi-Yau geometry by reconstructing the Noether-Lefschetz generators, which are vector-valued modular forms. There is an isomorphism between the latter objects and vector-valued lattice Jacobi forms, which relates them to the elliptic genera and twisted-twined elliptic genera of six- and five-dimensional Heterotic strings. The meromorphic Jacobi forms generate the dimensions of the refined cohomology of the Hilbert schemes of symmetric products of the fiber and allow us to refine the BPS indices in the fiber and therefore to obtain, conjecturally, actual state counts. Using the properties of the vector-valued lattice Jacobi forms we also provide a mathematical proof of the non-Abelian weak gravity conjecture for F-/M-theory compactified on this general class of fibered Calabi-Yau 3-folds.
