A functorial approach to orbifold lifts and flow defects in Abelian GLSMs

Schneider, Christian Paul Maria (2025): A functorial approach to orbifold lifts and flow defects in Abelian GLSMs. Dissertation, LMU München: Fakultät für Physik

Abstract

Quantum field theories (QFTs) have proven to be immensely successful in high energy physics, however, our present understanding of them is quite limited. While the perturbative approach to QFT is by now standing on a rigorous mathematical foundation, a comprehensive mathematical formulation of non-perturbative QFT is still missing to this date. Still, there are special kinds of non-perturbative QFTs that do admit such a mathematical formulation. These are topological and conformal field theories that can be axiomatized in a functorial manner, employing the language of categories. An important source for examples of such functorial field theories is string theory. String theory, originally intended to describe the strong nuclear force, later on developed into a potential candidate for a unified QFT of the fundamental forces including gravity. Beyond its phenomenological implications, throughout its history string theory served as a fertile ground for new ideas in theoretical physics and mathematics. The eponymous strings in string theory can be described by so called gauged linear sigma models (GLSMs). GLSMs admit topological subsectors which are captured by so called topological conformal field theories. At low energies GLSMs exhibit a rich phase structure making them an ideal testing ground to study defects and phase transitions. In this thesis we present a novel approach for the construction of defects lifting so called orbifold phases to their respective GLSM in a functorial manner. To this end we restrict our attention to a topological subsector of GLSMs with Abelian gauge groups. Our construction in particular allows us to transport boundary conditions i.e. branes from orbifold phases to the GLSM. We present an overview of topological field theories, introduce the topological B-model for GLSMs and discuss our construction for lift defects. Finally we demonstrate that our approach reproduces known results for brane transport and for flows in minimal models.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: mathematical physics, topological field theory, defects, gauged linear sigma models, Landau-Ginzburg
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 15. Mai 2025
• 1. Bericht­erstatter:in: Brunner, Ilka