Cobordism Classes and the Swampland

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.

35 pages, 6 figures; references added

References in corpus (3)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory

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• Cobordism Conjecture in AdS
• Stringy Bubbles Solve de Sitter Troubles
• Geometric Flow of Bubbles
• AdS Swampland Conjectures and Light Fermions
• Entanglement entropy and edge modes in topological string theory: I