The stack of Yang-Mills fields on Lorentzian manifolds

Benini, Marco; Schenkel, Alexander; Schreiber, Urs

Abstract

We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in [S. Hollander, Israel J. Math. 163, 93-124 (2008)], which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BGcon.

Citation

Benini, M., Schenkel, A., & Schreiber, U. (2018). The stack of Yang-Mills fields on Lorentzian manifolds. Communications in Mathematical Physics, 359(2), 765-820. https://doi.org/10.1007/s00220-018-3120-1

• Journal Article Type: Article
• Acceptance Date: Jan 19, 2018
• Online Publication Date: Mar 21, 2018
• Publication Date: 2018-04
• Deposit Date: Mar 14, 2018
• Publicly Available Date: Mar 21, 2018
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 359
• Issue: 2
• Pages: 765-820
• DOI: https://doi.org/10.1007/s00220-018-3120-1
• Keywords: Yang-Mills theory, globally hyperbolic Lorentzian manifolds, Cauchy problem, stacks, presheaves of groupoids, homotopical algebra, model categories
• Public URL: https://nottingham-repository.worktribe.com/output/929337
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00220-018-3120-1
• Additional Information: Received: 12 April 2017; Accepted: 19 January 2018; First Online: 21 March 2018
• Contract Date: Mar 14, 2018