On the intermediate Jacobian of M5-branes

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 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.

Towards natural and realistic E7 GUTs in F-theory

“…A great advantage of studying the stratification of Z is that the Hodge numbers of Z can be computed using the Hodge-Deligne numbers together with the stratification [39,95] (see also [96] for more recent review and applications). In our case where Z is smooth, the Hodge-Deligne numbers are just certain signed combinations of the Hodge numbers, but they behave nicely under disjoint unions and products.…”