On the Higher Categorical Structure of Topological Defects in Quantum Field Theories

2025/05/07 by Lukas Müller, Müller, Lukas · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2505.04761

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or Pin^±-structures, in terms of structured versions of higher dagger categories. This recovers all previously known results, including the description of oriented topological defects in 2-dimensional quantum field theories by pivotal bicategories. Assuming the stratified cobordism hypothesis, we prove our proposal for topological defects with stable tangential structures that admit a direct sum in fully extended topological quantum field theories.

Citations

• Orbifolds, higher dagger structures, and idempotents
• Global Structure in the Presence of a Topological Defect
• Manifestly unitary higher Hilbert spaces
• Dagger n-categories
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Orbifolds of topological quantum field theories
• Lectures on Generalized Symmetries
• Orbifold completion of 3-categories
• Dagger categories via anti-involutions and positivity
• Topological symmetry in quantum field theory
• The geometric cobordism hypothesis
• Q-system completion is a 3-functor
• Condensations in higher categories
• Fusion 2-categories and a state-sum invariant for 4-manifolds
• Factorization homology I: higher categories
• A stratified homotopy hypothesis
• Supersymmetric field theories and generalized cohomology
• Field theories with defects and the centre functor
• Topological Field Theory, Higher Categories, and Their Applications
• On the Classification of Topological Field Theories
• On Topological Defects

Cited by

• How to Build Anomalous (3+1)d Topological Quantum Field Theories

Related

• Orbifolds, higher dagger structures, and idempotents
• A higher category of cobordisms and topological quantum field theory
• Field theories with defects and the centre functor
• Topological symmetry in quantum field theory
• A general state-sum construction of 2-dimensional topological quantum field theories with defects