2006/08/08 by Eric Sharpe, E. Sharpe, Sharpe, E.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Computer science #FOS: Physical sciences #Flow (mathematics) #Functional renormalization group #Geometric and Algebraic Topology #Group (periodic table) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Independence (probability theory) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Physics #Presentation (obstetrics) #Quantum mechanics #Realization (probability) #Renormalization group #Statistics #String (physics) #Theoretical physics #Worldsheet #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0608056
27 pages, LaTeX, 2 figures, contribution to proceedings of Vienna homological mirror symmetry conference, June 2006; v2: refs added
openalex publication_date 2006/08/08 · arxiv created 2006/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this note we review how both derived categories and stacks enter physics. The physical realization of each has many formal similarities. For example, in both cases, equivalences are realized via renormalization group flow: in the case of derived categories, (boundary) renormalization group flow realizes the mathematical procedure of localization on quasi-isomorphisms, and in the case of stacks, worldsheet renormalization group flow realizes presentation-independence. For both, we outline current technical issues and applications.