2001/03/14 by W. Lerche, Lerche, W., Peter Mayr +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG
paper · pdf · doi:10.48550/arxiv.hep-th/0103114
29 pages, harvmac(b), 2 figs
arxiv created 2001/03/14 · openalex publication_date 2001/03/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The boundary chiral ring of a 2d gauged linear sigma model on a Kähler manifold X classifies the topological D-brane sectors and the massless open strings between them. While it is determined at small volume by simple group theory, its continuation to generic volume provides highly non-trivial information about the D-branes on X, related to the derived category D^\flat(X). We use this correspondence to elaborate on an extended notion of McKay correspondence that captures more general than orbifold singularities. As an illustration, we work out this new notion of McKay correspondence for a class of non-compact Calabi-Yau singularities related to Grassmannians.