Affine SU(N) algebra from wall-crossings

Details Affine SU(N) algebra from wall-crossings Affine SU(N) algebra from wall-crossings

2011-07-24

arxiv.org/abs/1107.4762v1

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 14 figures

Scientific paper

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.

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