Cobordism and string theory

Kneißl, Christian (2025): Cobordism and string theory. Dissertation, LMU München: Faculty of Physics

Abstract

Cobordism theory has quickly developed into a substantial tool to uncover non-perturbative physics in string theory. Initially developed as a framework in algebraic topology to study certain equivalence classes of manifolds, it has entered the study of consistent quantum gravity theories in recent years. In this thesis, we will focus on one application– the Cobordism Conjecture. Concretely, the Cobordism Conjecture ties non-trivial cobordism equivalence classes to a non-vanishing global symmetry, which has to be gauged or broken to ensure quantum gravitational consistency. This conjecture originates from the Swampland Program as part of a whole network of interconnected conjectures. The aim of this web of conjectures is to universally delineate the effective theories coupled to gravity that can be consistently completed to a theory of quantum gravity in the UV from those that cannot. As the prime example of a consistent theory of quantum gravity string theory provides a framework for gathering evidence in favor or against a particular conjecture. Especially in regards to the Cobordism Conjecture it can even uncover unknown features of string theory, which are much more obscure in traditional approaches to string theory. In the main part, we first explore the behavior of the Cobordism Conjecture under dimensional reduction on background manifolds. We then investigate two closely related string theories–typeI and its strong coupling heterotic dual–through the lens of the Cobordism Conjecture. Coincidentally, we extend the traditional decription of Dp-branes in type I to facilitate our description of the objects required to satisfy the Cobordism Conjecture. Finally, we use our insights from the previous calculation to present a construction that explains Shenker effects in heterotic string theories, a peculiar non-perturbative effect that has been conjectured to exist for any closed string theory, but has lacked a construction in both heterotic string theories for decades.

• Item Type: Theses (Dissertation, LMU Munich)
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 530 Physics
• Faculties: Faculty of Physics
• Language: English
• Date of oral examination: 26. February 2025
• 1. Referee: Blumenhagen, Ralph
• Signature of the printed copy: 0001/UMC 31086