Categorification of algebraic quantum field theories

Abstract

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen's universal algebra is developed and also computed for simple examples of 2AQFTs.

arXiv comment40 pages - Accepted for publication in Letters in Mathematical Physics

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Cited by in corpus (7)

• Snowmass White Paper: The Quest to Define QFT
• Lorentzian 2d CFT from the pAQFT perspective
• Lorentzian bordisms in algebraic quantum field theory
• Deformation Quantization via Categorical Factorization Homology
• On the equivalence of AQFTs and prefactorization algebras
• Extended Field Theories as higher Kaluza-Klein theories
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order