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 wallcrossings 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 CalabiYau three-fold

Takahiro Nishinakaa

Papers

Affine SU(N) algebra from wall-crossings