Supergeometry in locally covariant quantum field theory

Hack, Thomas-Paul, Hanisch, Florian and Schenkel, Alexander (2016) Supergeometry in locally covariant quantum field theory. Communications in Mathematical Physics, 342 (2). pp. 615-673. ISSN 1432-0916

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In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.

Item Type: Article
Additional Information: The final publication is available at Springer via
Keywords: supergeometry, algebraic quantum field theory, locally covariant quantum field theory, enriched category theory
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
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Depositing User: Schenkel, Dr Alexander
Date Deposited: 06 Mar 2017 09:15
Last Modified: 04 May 2020 17:39

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