The stack of Yang-Mills fields on Lorentzian manifolds

Marco Benini, Alexander Schenkel, Urs Schreiber
April 05, 2017
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 $\mathrm{B}G_\mathrm{con}$.
open access link Commun. Math. Phys. (2018)
%%% contains utf-8, see: http://inspirehep.net/info/faq/general#utf8 %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Benini:2017zjv, author = "Benini, Marco and Schenkel, Alexander and Schreiber, Urs", title = "{The Stack of Yang–Mills Fields on Lorentzian Manifolds}", journal = "Commun. Math. Phys.", volume = "359", year = "2018", number = "2", pages = "765-820", doi = "10.1007/s00220-018-3120-1", eprint = "1704.01378", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1704.01378;%%" }

Keywords: 
Yang-Mills theory, globally hyperbolic Lorentzian manifolds, Cauchy problem, stacks, presheaves of groupoids, homotopical algebra, model categories