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

Journal of High Energy Physics, Jun 2018

Abstract M-theory on compact eight-manifolds with 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 Spin(7)-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four-fold and a G2-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 G2-holonomy manifold, which are shown to be precisely the recently discovered twisted-connected sum constructions.

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Andreas P. Braun, Sakura Schäfer-Nameki. Spin(7)-manifolds as generalized connected sums and 3d $$\mathcal{N}=1$$ theories, Journal of High Energy Physics, 2018, 103, DOI: 10.1007/JHEP06(2018)103