Affine SU(N) algebra from wall-crossings

TL;DR

This paper explores the connection between instanton counting on ALE spaces and BPS state counting on toric Calabi-Yau three-folds, revealing affine SU(N) algebra structures through wall-crossing phenomena.

Contribution

It demonstrates that affine SU(N) algebra characters naturally emerge in wall-crossings of D4-D2-D0 states in a Calabi-Yau setting, linking algebraic structures to BPS state dynamics.

Findings

Affine SU(N) algebra character appears in wall-crossings.

Wall-crossing formula applies to D4-D2-D0 states.

Connection between instanton counting and BPS states established.

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.