We consider consequences of triviality of cobordism classes and anomaly cancellation in supergravity theories in d > 6. We argue that this leads to the existence of certain defects which we call “I-folds” (a generalization of orientifolds). The requirement that compactifications to lower dimensions involving these defects be anomaly free leads to conditions on the higher dimensional theory. We show that in theories with 16 supercharges in d > 6 this leads to restrictions on the rank of the allowed gauge groups and thus provides an explanation for the observed restrictions in known string theory constructions. In particular, in eight and nine dimensions the only solutions to our constraints are precisely the ones realized in string theory compactifications. We also use these techniques to place constraints on the global structure of the gauge group in eight and nine dimensions.

在d> 6中，我们考虑了同构主义类别的琐碎性和超重力理论的异常抵消的后果。我们认为，这导致了某些缺陷的存在，我们称其为“ I形折叠”（定向的广义化）。压实到涉及这些缺陷的较低尺寸的要求无异常的要求导致了高尺寸理论的条件。我们证明在d>具有16个增压的理论中如图6所示，这导致对允许的量规组的等级的限制，从而提供了对已知弦理论构造中观察到的限制的解释。特别是，在八维和九维中，对我们的约束的唯一解决方案正是弦理论压缩中实现的解决方案。我们还使用这些技术在八维和九维上对量规组的全局结构施加约束。