Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories

Abstract

M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four-fold and a $G_2$-holonomy manifold times a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a cylinder. The generalized connected sum construction is first exemplified for Joyce orbifolds, and is then used to construct examples of new compact manifolds with $\mathrm{Spin}(7)$-holonomy. In instances when there is a K3-fibration of the $\mathrm{Spin}(7)$-manifold, we test the spectra using duality to heterotic on a $T^3$-fibered $G_2$-holonomy manifold, which are shown to be precisely the recently discovered twisted-connected sum constructions.

49 pages, 4 figures; v2: added references

References in corpus (4)

• Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• Deformations of asymptotically cylindrical G_2 manifolds
• Heterotic strings on G_2 orbifolds

Cited by in corpus (11)

• F-theory and Dark Energy
• Pixelated Dark Energy
• Living on the walls of super-QCD
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• An $\mathcal{N}=1$ 3d-3d Correspondence
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• On Mirror Maps for Manifolds of Exceptional Holonomy
• Geometric Unification of Higgs Bundle Vacua
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums