Discrete symmetries of Calabi–Yau hypersurfaces in toric four-folds

Journal article

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)≤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 ℤ₂×ℤ₂ symmetry where only one of the ℤ₂ factors was previously known. In addition, a new freely-acting ℤ₂ 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.

Authors: Braun, A; Lukas, A; Sun, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Verlag
• Journal: Communications in Mathematical Physics
• Volume: 360
• Issue: 3
• Pages: 935–984
• Publication date: 2017-12-12
• Acceptance date: 2017-10-11
• DOI: 10.1007/s00220-017-3052-1
• EISSN: 1432-0916
• ISSN: 0010-3616