Looking for structure in the cobordism conjecture

Andriot, David; Carqueville, Nils; Cribiori, Niccolò

doi:10.21468/SciPostPhys.13.3.071

SciPost Physics

Looking for structure in the cobordism conjecture

David Andriot, Nils Carqueville, Niccolò Cribiori

SciPost Phys. 13, 071 (2022) · published 28 September 2022

doi: 10.21468/SciPostPhys.13.3.071
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.3.071
TI  - Looking for structure in the cobordism conjecture
PY  - 2022/09/28
UR  - https://scipost.org/SciPostPhys.13.3.071
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 3
SP  - 071
A1  - Andriot, David
AU  - Carqueville, Nils
AU  - Cribiori, Niccolò
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.13.3.071,
	title={{Looking for structure in the cobordism conjecture}},
	author={David Andriot and Nils Carqueville and Niccolò Cribiori},
	journal={SciPost Phys.},
	volume={13},
	pages={071},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.3.071},
	url={https://scipost.org/10.21468/SciPostPhys.13.3.071},
}

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Funders for the research work leading to this publication

Alexander von Humboldt-Stiftung / Alexander von Humboldt Foundation
Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]