2009/07/02 by Chien‐Hao Liu, Chien-Hao Liu, Shing-Tung Yau +3 · 1 citation
Mathematics · Physics and Astronomy · #14A22 #14E15 #16G30 #81T30 #81T75 #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG #msc:14A22 #msc:14E15 #msc:16G30 #msc:81T30 #msc:81T75
paper · pdf · doi:10.48550/arxiv.0907.0268
23+2 pages, 4 figures
arxiv created 2009/07/02 · openalex publication_date 2009/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold Y can be obtained via morphisms from Azumaya points are given. This should be compared with the quantum-field-theoretic/D-brany picture of deformations and resolutions of a conifold via a D-brane probe sitting at the conifold singularity in the work of Klebanov and Witten [K-W] (arXiv:hep-th/9807080) and Klebanov and Strasser [K-S] (arXiv:hep-th/0007191). A comparison with resolutions via noncommutative desingularizations is given in the end.