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.

arXiv comment35 pages, 6 figures; references added

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Cited by in corpus (36)

• Lectures on the Swampland Program in String Compactifications
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Review of the No-Boundary Wave Function
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Baby Universes, Holography, and the Swampland
• Finiteness and the Swampland
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Holo-ween
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• Disorder Averaging and its UV (Dis)Contents
• Classifying Calabi-Yau threefolds using infinite distance limits
• Asymptotic Observables and the Swampland
• Special Geometry and the Swampland
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• A universal formula for the density of states in theories with finite-group symmetry
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Cobordism and Deformation Class of the Standard Model
• M/F-Theory as Mf-Theory
• Ultra Unification
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Gravitational Solitons and Completeness
• Proton Stability: From the Standard Model to Beyond Grand Unification
• Modular Curves and the Refined Distance Conjecture
• Cobordism Conjecture in AdS
• Stringy Bubbles Solve de Sitter Troubles
• Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high energy RS-II Braneworld
• Geometric Flow of Bubbles
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lorentz violating inflation and the Swampland
• Lectures in Quantum Gravity
• Monopole Breaking of Chern-Weil Symmetries
• AdS Swampland Conjectures and Light Fermions
• Entanglement entropy and edge modes in topological string theory: I
• Implications of single field inflation in general cosmological scenarios on the nature of dark energy given the swampland conjectures
• Toroidal $\&$ orbifold compactifications at large D and D-duality