2024/12/10 by Benini, Marco, Carmona, Victor, Grant-Stuart, Alastair +1 · 1 citation
#18Nxx #53C50 #81Txx #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2412.07318
This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1.) a structural implementation of the additivity property used in earlier approaches and 2.) a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal 1-category, this yields a generalization of the equivalence theorem from [Commun. Math. Phys. 377, 971 (2019)]. In the case where the target is the symmetric monoidal ∞-category of cochain complexes, we obtain a reduction of the global ∞-categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between 1-categories exhibit ∞-localizations, however the available detection criteria are inconclusive in our case.