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arXiv · 2211.00210

On the intermediate Jacobian of M5-branes

Patrick Jefferson·Manki Kim
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Abstract

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.

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Patrick Jefferson, Manki Kim. 2023-05-04. On the intermediate Jacobian of M5-branes. https://arxiv.org/abs/2211.00210

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