2009/01/03 by Chien‐Hao Liu, Chien-Hao Liu, Shing-Tung Yau +3 · 4 citations
Mathematics · Physics and Astronomy · #14E15 #81T30 #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) #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG #msc:14E15 #msc:81T30
paper · pdf · doi:10.48550/arxiv.0901.0342
20 pages, 2 figures
arxiv created 2009/01/03 · openalex publication_date 2009/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this continuation of [L-Y1] and [L-L-S-Y], we explain how the Azumaya structure on D-branes together with a netted categorical quotient construction produces the same resolution of ADE orbifold singularities as that arises as the vacuum manifold/variety of the supersymmetric quantum field theory on the D-brane probe world-volume, given by Douglas and Moore [D-M] under the string-theory contents and constructed earlier through hyper-Kähler quotients by Kronheimer and Nakajima. This is consistent with the moral behind this project that Azumaya-type structure on D-branes themselves -- stated as the Polchinski-Grothendieck Ansatz in [L-Y1] -- gives a mathematical reason for many originally-open-string-induced properties of D-branes.