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arXiv · 2110.03696

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

Sebastián Franco·Alessandro Mininno·Ángel M. Uranga·Xingyang Yu
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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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Sebastián Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu. 2021-10-07. 2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds. https://doi.org/10.1007/jhep03(2022)150

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