Open-Closed Correspondence of K-theory and Cobordism

Abstract

Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, which can be considered as the physical manifestation of a generalisation of the classic Conner--Floyd isomorphism. The picture is exemplified by the relations between KO-groups and Spin-cobordisms and between K-groups and Spin${}^c$-cobordisms. Global symmetries related by such isomorphism are eventually gauged. By combining K-theory and cobordism, we recover then tadpole cancellation conditions in type I string theory and F-theory from a bottom-up perspective.

arXiv comment36 pages, 2 figures, 5 tables; v2: 35 pages, 1 figure, 5 tables, substantial revision of mainly section 5

References in corpus (27)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• D-Branes And K-Theory
• The Swampland: Introduction and Review
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Constraints on Low-Dimensional String Compactifications
• K3 Orientifolds
• Orientifold Limit of F-theory Vacua
• D-brane probes, RR tadpole cancellation and K-theory charge
• Dai-Freed anomalies in particle physics
• Point-like Instantons on K3 Orbifolds
• Brane solutions in strings with broken supersymmetry and dilaton tadpoles
• An Orientifold of Type-IIB Theory on $K3$
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• 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
• Dilaton Tadpoles, Warped Geometries and Large Extra Dimensions for Non-Supersymmetric Strings
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• On Ramond-Ramond fields and K-theory
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• Dynamical Tadpoles, Stringy Cobordism, and the SM from Spontaneous Compactification
• Equivariant Cohomotopy implies orientifold tadpole cancellation
• Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
• Branes, U-folds and hyperelliptic fibrations
• Type IIB flux vacua from G-theory I
• The fate of the type I non-BPS D7-brane
• A Note on the dS Swampland Conjecture, Non-BPS branes and K-theory

Cited by in corpus (6)

• Dynamical Cobordism of a Domain Wall and its Companion Defect 7-brane
• IIB Explored: Reflection 7-Branes
• Dimensional Reduction of Cobordism and K-theory
• Looking for structure in the cobordism conjecture
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Metastable vacua from torsion and machine learning