Abstract
We analyze freely-acting discrete symmetries of Calabi–Yau three-folds defined as hypersurfaces in ambient toric four-folds. An algorithm that allows the systematic classification of such symmetries which are linearly realised on the toric ambient space is devised. This algorithm is applied to all Calabi–Yau manifolds with \({h^{1,1}(X)\leq 3}\) obtained by triangulation from the Kreuzer–Skarke list, a list of some 350 manifolds. All previously known freely-acting symmetries on these manifolds are correctly reproduced and we find five manifolds with freely-acting symmetries. These include a single new example, a manifold with a \({\mathbb{Z}_2\times\mathbb{Z}_2}\) symmetry where only one of the \({\mathbb{Z}_2}\) factors was previously known. In addition, a new freely-acting \({\mathbb{Z}_2}\) symmetry is constructed for a manifold with \({h^{1,1}(X)=6}\). While our results show that there are more freely-acting symmetries within the Kreuzer–Skarke set than previously known, it appears that such symmetries are relatively rare.
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Braun, A.P., Lukas, A. & Sun, C. Discrete Symmetries of Calabi–Yau Hypersurfaces in Toric Four-Folds. Commun. Math. Phys. 360, 935–984 (2018). https://doi.org/10.1007/s00220-017-3052-1
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DOI: https://doi.org/10.1007/s00220-017-3052-1