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

TL;DR

The paper develops a framework to realize non-supersymmetric four-dimensional effective theories by F-theory on Spin(7) manifolds, supported by a proposed M-theory/F-theory duality on Spin(7) spaces times an interval. Spin(7) backgrounds are constructed as anti-holomorphic quotients of elliptically fibered Calabi–Yau fourfolds, and the authors derive a 3d $\mathcal{N}=1$ effective action with flux, then match it to a finite-interval reduction of a non-supersymmetric 4d theory to fix a minimal set of 4d couplings in terms of geometric data. They further analyze the CY quotient limits, parity structures, and the F-theory lift, providing a concrete route to connect M-theory reductions to 4d physics through the interval, while discussing the weak coupling Type IIB interpretation and implications for charged matter. The work highlights how Spin(7) geometry can be used to study controlled SUSY-breaking scenarios and clarifies the role of boundary conditions and interval size in shaping the low-energy spectrum and couplings. Overall, it opens a path to exploring non-supersymmetric string vacua with geometric control, albeit with open questions about backreaction, singularity resolution, and full 4d Wilsonian 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.

Figures (2)

• Figure 1: Summary of the effective actions considered in this work. The left column corresponds to the M-theory side of the duality \ref{['new_dual']}, while the right column corresponds to the F-theory side. The comparison between the 3d $\mathcal{N}=1$ theories is performed in the case in which the Spin(7) manifold arises as an anti-holomorphic quotient of an elliptically fibered Calabi-Yau fourfold. We consider a fibration structure that yields a simple non-Abelian gauge group. The match of 3d actions is carried out in the Coulomb branch at the level of zero modes.
• Figure 2: Construction of Spin(7) manifolds by using Calabi-Yau fourfolds with anti-holomorphic involutions.