Cobordism conjecture, anomalies, and the String Lamppost Principle

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.

Automated summary

We explored triviality of cobordism classes and anomaly cancellation in supergravity theories in d > 6, leading to the existence of defects called I-folds. The compactification conditions to lower dimensions with these defects being anomaly-free impose restrictions on higher dimensional theories, particularly on the allowed rank of gauge groups. These restrictions explain observed limitations in string theory constructions, with the solutions in eight and nine dimensions matching string theory compactifications.Constraints on the global structure of the gauge group in eight and nine dimensions were also derived using these techniques.