A bstract We initiate the geometric engineering of 2d $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = (0 , 1) theories as real slices of $$ \mathcal{N} $$ 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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Orientifold Calabi-Yau threefolds with divisor involutions and string landscape
A bstract We establish an orientifold Calabi-Yau threefold database for h 1 , 1 ( X ) ≤ 6 by considering non-trivial ℤ 2 divisor exchange involutions, using a toric Calabi-Yau database ( www.rossealtman.com/tcy ). We first determine the topology for each individual divisor (Hodge diamond), then identify and classify the proper involutions which are globally consistent across all disjoint phases of the Kähler cone for each unique geometry. Each of the proper involutions will result in an orientifold Calabi-Yau manifold. Then we clarify all possible fixed loci under the proper involution, thereby determining the locations of different types of O -planes. It is shown that under the proper involutions, one typically ends up with a system of O 3 /O 7-planes, and most of these will further admit naive Type IIB string vacua. The geometries with freely acting involutions are also determined. We further determine the splitting of the Hodge numbers into odd/even parity in the orbifold limit. The final result is a class of orientifold Calabi-Yau threefolds with non-trivial odd class cohomology ( $$ {h}_{-}^{1,1} $$ h − 1 , 1 ( X/σ * ) ≠ 0).
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- Award ID(s):
- 1913328
- PAR ID:
- 10353339
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 3
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP03(2022)087
