2011/07/24 by Takahiro Nishinaka, Satoshi Yamaguchi, Nishinaka, Takahiro +1
Mathematics · Physics and Astronomy · #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) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1107.4762
openalex publication_date 2011/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the relation between the instanton counting on ALE spaces and the BPS state counting on a toric Calabi-Yau three-fold. We put a single D4-brane on a divisor isomorphic to AN-1-ALE space in the Calabi-Yau three-fold, and evaluate the discrete changes of BPS partition function of D4-D2-D0 states in the wall-crossing phenomena. In particular, we find that the character of affine SU(N) algebra naturally arises in wall-crossings of D4-D2-D0 states. Our analysis is completely based on the wall-crossing formula for the d=4, N=2 supersymmetric theory obtained by dimensionally reducing the Calabi-Yau three-fold.