论文标题
在M5-branes的中间雅各布
On the intermediate Jacobian of M5-branes
论文作者
论文摘要
我们研究了椭圆形的calabi-yau中的垂直分隔线的欧几里得M5-溴化物的M/F理论四倍压缩，这些压缩是允许SEN限制的。我们将这些calabi-yau四倍构造为椭圆形的椭圆振动，上面是旋转曲面的calabi-yau三倍。我们设计了一种方法来分析这四倍的垂直除法的Hodge结构（以及中间雅各布的维度），仅使用从O3/O7 calabi-yau erientientifold上的IIB类型的数据中获得的数据。我们的方法利用了简单的组合公式（我们证明的）用于calabi-yau orientientifolds及其主要的复值分隔剂的近似霍奇数，以及相应的椭圆形的calabi-yau-yau-yau-yau-yau-yau fourdold的垂直分裂特征的公式。我们针对Euler特征的公式包括一个猜想的校正项，该术语说明了尖端终端$ \ mathbb {z} _2 $奇异性的贡献，与扰动O3平面相对应。我们在许多明确的示例中检查我们的猜想，并与直接计算的结果找到完美的一致性。
We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal $\mathbb{Z}_2$ singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.
