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.
Highlights
Page 3 of 49 35 loss of information when passing from X to its function algebra O(X )
To understand the example below, let us recall that stacks are higher categorical spaces that are compared by a suitable kind of weak equivalences, see, e.g., [46] for the relevant model category structure
Let us explain in more detail the content of the present paper and the results we obtain: In Sect. 2, we introduce an equivalent perspective on ordinary algebraic quantum field theories (AQFTs) as prefactorization algebras [17] with values in the symmetric monoidal category AlgK of associative and unital K-algebras
Summary
Page 3 of 49 35 loss of information when passing from X to its function algebra O(X ). The feature that stacks are in general not completely determined by their function dg-algebras is well known to algebraic geometers, see, e.g., [10] for an excellent overview, who have proposed the following interesting solution: Instead of assigning a function dg-algebra O(X ) to a space or stack X , it is better to assign the category QCoh(X ) of quasi-coherent sheaves on X. The latter is a locally presentable symmetric monoidal K-linear category that should be interpreted roughly as the category of vector bundles over X. By Tannakian reconstruction, RepK(G) encodes the full information about the group G, QCoh(BG) is much
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