Affine SU(N) algebra from wall-crossings

Abstract

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 A_{N-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.

34 pages, 14 figures

References in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Wall crossing in local Calabi Yau manifolds
• Crossing the Wall: Branes vs. Bundles
• Curve counting and instanton counting
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Ample D4-D2-D0 Decay
• Statistical model and BPS D4-D2-D0 counting
• Fragmenting D4 branes and coupled q-deformed Yang Mills