Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds

TL;DR

This paper introduces a method to derive non-supersymmetric 4D effective actions from F-theory compactified on Spin(7) manifolds, utilizing dualities with M-theory and geometric constructions.

Contribution

It proposes a duality between M-theory on Spin(7) manifolds and F-theory on the same manifolds times an interval, enabling the study of non-supersymmetric compactifications.

Findings

Derived 3D M-theory effective action on Spin(7) manifolds with fluxes.

Established a correspondence with 4D non-supersymmetric theories via interval reduction.

Provided geometric data for constructing 4D effective actions.

Abstract

We propose a novel approach to obtain non-supersymmetric four-dimensional effective actions by considering F-theory on manifolds with special holonomy Spin(7). To perform such studies we suggest that a duality relating M-theory on a certain class of Spin(7) manifolds with F-theory on the same manifolds times an interval exists. The Spin(7) geometries under consideration are constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic and isometric involution. The three-dimensional minimally supersymmetric effective action of M-theory on a general Spin(7) manifold with fluxes is determined and specialized to the aforementioned geometries. This effective theory is compared with an interval Kaluza-Klein reduction of a non-supersymmetric four-dimensional theory with definite boundary conditions for all fields. Using this strategy a minimal set of couplings of the four-dimensional low-energy effective actions is obtained in terms of the Spin(7) geometric data. We also discuss briefly the string interpretation in the Type IIB weak coupling limit.