Categorification of algebraic quantum field theories

Marco Benini, Marco Perin, Alexander Schenkel, Lukas Woike
March 30, 2020
This paper develops a novel 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.

algebraic quantum field theory, 2-categories, 2-operads, quasi-coherent sheaves, locally presentable linear categories, categorified orbifold theories, local-to-global extensions