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.
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Franco, S., Mininno, A., Uranga, Á.M. et al. 2d \( \mathcal{N} \) = (0, 1) gauge theories and Spin(7) orientifolds. J. High Energ. Phys. 2022, 150 (2022). https://doi.org/10.1007/JHEP03(2022)150
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DOI: https://doi.org/10.1007/JHEP03(2022)150