On effective F-theory action in type IIA compactifications

TL;DR

This paper refines the understanding of F-theory's effective action in type IIA compactifications, proposing a geometric formulation and confirming a conjecture in specific cases, linking it to elliptic cohomology.

Contribution

It defines the geometric term of the F-theory effective action in type IIA compactifications and proves a conjecture relating to elliptic cohomology under certain conditions.

Findings

Defined the geometric term of F-theory effective action.

Proved a version of the Kriz-Sati conjecture when the first Pontrjagin class vanishes.

Extended Diaconescu-Moore-Witten arguments to this special case.

Abstract

Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of spacetime vanishes, we also prove a version of the Kriz-Sati conjecture by extending the arguments of Diaconescu-Moore-Witten. We also briefly discuss why even this special case contains interesting examples.