Cobordism Classes and the Swampland

TL;DR

This paper argues that quantum gravity theories with non-trivial cobordism classes are inconsistent with the Swampland conjecture, linking cobordism triviality to the existence of specific stringy defects.

Contribution

It introduces a novel connection between cobordism classes, global symmetries, and string defects, proposing that non-trivial cobordism classes place theories in the Swampland.

Findings

Non-trivial cobordism classes imply the need for certain string defects.

Evidence suggests some defects can preserve supersymmetry.

Predicts new non-supersymmetric defects in string theory.

Abstract

We argue that any proposed quantum theory of gravity with non-trivial cobordism classes in the space of configurations belongs to the Swampland. The argument is based on the assumption that there are no global symmetries in a consistent theory of quantum gravity. The triviality of the cobordism classes requires the existence of certain stringy defects that trivialize the potential cobordism classes. We provide evidence for this conjecture by identifying those defects demanded by this argument that could preserve supersymmetry, and predict the existence of new non-supersymmetric defects in string theory.