Swampland conjectures and infinite flop chains
Swampland conjectures and infinite flop chains
复制标题
沼泽猜想和无限失败链
作者：
Callum R. Brodie;A. Constantin;A. Lukas;Fabian Ruehle
本文在卡-丘三重紧致化的M-理论的背景下研究了量子引力的沼泽地结构。简单地说，这种紧化的模空间包含任意测地线长度的路径，它们穿过任意多个凯勒锥，沿着这些凯勒锥，低能谱几乎保持不变。在卡-丘流形的无限链只涉及有限个同构类的情况下，模空间具有无限离散对称性，它与由触发器连接的同构流形有关。这是11维庞加莱对称性的残余，因此被测量，因为它必须由非整体对称性猜想。与沼泽地距离猜想的明显矛盾因此在除以这种离散对称性后得到解决。如果触发器序列涉及无穷多个非同构流形，则此解决方案不再可用。然而，如果卡-丘三重性的川端-莫里森猜想成立，这种情况就不会发生。相反，沼泽地距离猜想，当应用于无限翻转链时，在一个合理的假设下，Kähler锥的直径意味着川俣-莫里森猜想。
We investigate swampland conjectures for quantum gravity in the context of M-theory compactified on Calabi-Yau threefolds which admit infinite sequences of flops. Naively, the moduli space of such compactifications contains paths of arbitrary geodesic length traversing an arbitrarily large number of Kähler cones, along which the low-energy spectrum remains virtually unchanged. In cases where the infinite chain of Calabi-Yau manifolds involves only a finite number of isomorphism classes, the moduli space has an infinite discrete symmetry which relates the isomorphic manifolds connected by flops. This is a remnant of the 11D Poincare symmetry and consequently gauged, as it has to be by the no-global symmetry conjecture. The apparent contradiction with the swampland distance conjecture is hence resolved after dividing by this discrete symmetry. If the flop sequence involves infinitely many non-isomorphic manifolds, this resolution is no longer available. However, such a situation cannot occur if the Kawamata-Morrison conjecture for Calabi-Yau threefolds is true. Conversely, the swampland distance conjecture, when applied to infinite flop chains, implies the Kawamata-Morrison conjecture under a plausible assumption on the diameter of the Kähler cones.