Cobordism Conjecture, Anomalies, and the String Lamppost Principle

TL;DR

This paper explores how cobordism and anomaly cancellation in high-dimensional supergravity theories imply the existence of defects called I-folds, constraining gauge groups and aligning with known string theory solutions.

Contribution

It introduces the concept of I-folds from cobordism and anomaly considerations, providing new constraints on gauge groups in supergravity and string theories in dimensions above six.

Findings

Restrictions on gauge group ranks in 8 and 9 dimensions.

Only known string theory solutions satisfy the derived constraints.

Constraints on the global structure of gauge groups in high dimensions.

Abstract

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.