Leiden University Student Repository

Knevel, Ilse (2025)

Symmetry Breaking and Topological Defects: A Theoretical Framework

Bachelor thesis | Wiskunde (BSc)

Topological defects are field excitations that are stabilised by topological obstructions. They emerge in symmetry breaking phase transitions. Such transitions are mathematically described by quotients of Lie groups and result in a vacuum manifold. Topological defects can be characterised by the topology of the vacuum manifold using homotopy theory. As such, the study of topological defects presents a surprising application of the theoretical field of algebraic topology. This thesis provides the mathematical background of Lie groups and homotopy theory as well as the physical background of field theory and symmetry breaking needed to understand topological defects. We look at some examples of topological defects and the grand unified theory of SU(5). We will conclude that strings cannot form as a result of symmetry breaking phase transitions of the grand unified theory of SU(5).

Topological Defects

Symmetry breaking

Yang Mills theory

Lie groups and algebras

Author

Knevel, Ilse

Faculty

Faculty of Science

Specialisation

AMG

Supervisors

Patil, S.P.
Pasquotto, F.

ECTS Credits

24

Language

en