Wall-crossing, Toric divisor and Seiberg duality

Abstract

We study the wall-crossing phenomena of BPS D4-D2-D0 states on the conifold and orbifold C^2/Z_2, from the viewpoint of the quiver quantum mechanics on the D-branes. The Kahler moduli dependence of the BPS index is translated into the FI parameter dependence of the Witten index. The wall-crossing phenomena are related to the Seiberg dualities of the quiver quantum mechanics. All the differences from the D6-D2-D0 case arise from the additional superpotential and "anti-quark" induced by the D4-brane. When the D-branes are on the conifold, the flop transition changes the duality cascade. When the D-branes are on the orbifold C^2/Z_2, the generating function of the Witten index is always given by a character of the affine SU(2) algebra. Both are consistent with the wall-crossing formula for BPS indices.

25 pages, 8 figures

References in corpus (10)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Dimer models and toric diagrams
• Wall-Crossing from Boltzmann Black Hole Halos
• Seiberg Duality for Quiver Gauge Theories
• Crystal Melting and Toric Calabi-Yau Manifolds
• Wall crossing in local Calabi Yau manifolds
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• D-Branes, Pi-Stability and Theta-Stability
• Statistical model and BPS D4-D2-D0 counting
• A note on statistical model for BPS D4-D2-D0 states