Looking for structure in the cobordism conjecture

Abstract

The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.

arXiv comment41 pages; v2: minor changes

References in corpus (49)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• The Swampland: Introduction and Review
• Counting Flux Vacua
• Double Field Theory: A Pedagogical Review
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Monopoles, Duality, and String Theory
• Constraints on symmetry from holography
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• A ten-dimensional action for non-geometric fluxes
• Dai-Freed anomalies in particle physics
• Exotic Branes in String Theory
• Exotic branes and non-geometric backgrounds
• Heisenberg Groups and Noncommutative Fluxes
• The web of swampland conjectures and the TCC bound
• Čech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
• String universality in ten dimensions
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• A violation of global symmetries from replica wormholes and the fate of black hole remnants
• Global symmetry, Euclidean gravity, and the black hole information problem
• Branes and the Swampland
• Non-geometric backgrounds in string theory
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• A note on Gauge Theories Coupled to Gravity
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• Four Dimensional $\mathcal{N}=4$ SYM and the Swampland
• Finiteness and the Swampland
• Refining the boundaries of the classical de Sitter landscape
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• The anomaly that was not meant IIB
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• Moduli Space Holography and the Finiteness of Flux Vacua
• Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity
• Dynamical Tadpoles, Stringy Cobordism, and the SM from Spontaneous Compactification
• Fivebrane Structures
• Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
• Nothing really matters
• Open-Closed Correspondence of K-theory and Cobordism
• New supersymmetric vacua on solvmanifolds
• Bubbles of Nothing and Supersymmetric Compactifications
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Topological violation of global symmetries in quantum gravity
• de Sitter Bubbles and the Swampland
• Ninebrane structures
• Topological T-Duality for Twisted Tori

Cited by in corpus (7)

• Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes
• Shedding black hole light on the emergent string conjecture
• Revisiting Dudas-Mourad compactifications
• Dimensional Reduction of Cobordism and K-theory
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Gravitational Background of Alice-Vortices and R7-Branes