Spin(7)-manifolds as generalized connected sums and 3d N=1 $$ \mathcal{N}=1 $$ theories

Abstract

Abstract M-theory on compact eight-manifolds with Spin(7)-holonomy is a framework for geometric engineering of 3d N=1 $$ \mathcal{N}=1 $$ gauge theories coupled to gravity. We propose a new construction of such 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 Spin(7)-holonomy. In instances when there is a K3-fibration of the 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.

Keywords

• Differential and Algebraic Geometry
• String Duality
• M-Theory