Cobordism Conjecture, Anomalies, and the String Lamppost Principle

TL;DR

The paper investigates why consistent theories with 16 supercharges in dimensions $d>6$ exhibit constrained gauge structure. By combining the Cobordism Conjecture with anomaly cancellation, the authors argue that I-fold defects must exist to trivialize cobordism classes on non-orientable backgrounds, and that anomaly inflow from compactifications to lower dimensions imposes precise rank constraints on the higher-dimensional gauge groups. In nine, eight, and seven dimensions, they derive rank congruences $r\equiv 1\pmod{8}$, $r\equiv 2\pmod{8}$, and $r\equiv 1\pmod{2}$, respectively, which align with known string theory constructions (e.g., ranks $1,9,17$ in 9d; $2,10,18$ in 8d; and odd ranks in 7d). They further constrain the global structure of gauge groups in 8d/9d and discuss charge lattices, supporting the String Lamppost Principle. The work suggests that a small set of general principles suffices to reproduce the string landscape in $d>7$ and offers avenues for further exploration of I-folds and lattice symmetries.

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.