Supergeometry in locally covariant quantum field theory

Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander

Abstract

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.

Citation

Hack, T., Hanisch, F., & Schenkel, A. (2016). Supergeometry in locally covariant quantum field theory. Communications in Mathematical Physics, 342(2), 615-673. https://doi.org/10.1007/s00220-015-2516-4

• Journal Article Type: Article
• Acceptance Date: Sep 16, 2015
• Online Publication Date: Dec 1, 2015
• Publication Date: 2016-03
• Deposit Date: Mar 6, 2017
• Publicly Available Date: Mar 6, 2017
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 342
• Issue: 2
• Pages: 615-673
• DOI: https://doi.org/10.1007/s00220-015-2516-4
• Keywords: supergeometry, algebraic quantum field theory, locally covariant quantum field theory, enriched category theory
• Public URL: https://nottingham-repository.worktribe.com/output/778366
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00220-015-2516-4
• Related Public URLs: https://arxiv.org/abs/1501.01520
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-015-2516-4