论文标题
全态异常，四倍和磁通
Holomorphic Anomalies, Fourfolds and Fluxes
论文作者
论文摘要
我们研究了带有背景通量的卡拉比Yau四倍的弦弦压缩的分区函数的全态异常。对于椭圆四倍，分区函数具有替代解释为n = 1个超对称弦理论的椭圆形属，或者是针对具有磁通量的四倍的相对Gromov-witten不变性的函数。我们通过从拓扑字符串的BCOV形式上开始，将它们转化为几何术语来得出霍明型异常方程。结果可以重铸为模块化和椭圆形的异常方程。作为一项新功能，与三倍相比，我们发现了一个额外的贡献，该贡献由引力后代不变剂提供。这会导致异常方程中的线性项，该方程支持衍生物映射的代数在各个通量扇区的分区函数之间。这些几何特征由准雅各比形式的某些属性反映。我们还从世界表理论的角度提供了物理学的解释。
We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N=1 supersymmetric string theories in four dimensions, or as generating functions for relative Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory.
