2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds

Abstract

We initiate the geometric engineering of 2d $\mathcal{N}=(0,1)$ gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity. We refer to such constructions as Spin(7) orientifolds. Spin(7) orientifolds explicitly realize the perspective on 2d $\mathcal{N}=(0,1)$ theories as real slices of $\mathcal{N}=(0,2)$ ones. Remarkably, this projection is geometrically realized as Joyce's construction of Spin(7) manifolds via quotients of Calabi-Yau 4-folds by anti-holomorphic involutions. We illustrate this construction in numerous examples with both orbifold and non-orbifold parent singularities, discuss the role of the choice of vector structure in the orientifold quotient, and study partial resolutions.

v2: added references + typos corrected v1: 49 pages + 1 appendix

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Cited by in corpus (5)

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• On the Master Space for Brane Brick Models
• $\mathcal{N}=1$ conformal dualities from unoriented chiral quivers
• Tetrahedron duality