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Affine SU(N) algebra from wall-crossings
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In this article, the relation between instanton counting on ALE spaces and BPS state counting on a toric Calabi-Yau threefold was studied, and it was shown that the character of affine SU(N) algebra naturally arises in wallcrossings of D4-D2-D0 states.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 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-foldread more
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Infinite Dimensional Lie Algebras
TL;DR: The invariant bilinear form and the generalized casimir operator are integral representations of Kac-Moody algebras and the weyl group as mentioned in this paper, as well as a classification of generalized cartan matrices.
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A Strong coupling test of S duality
Cumrun Vafa,Edward Witten +1 more
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Edward Witten,David I. Olive +1 more
TL;DR: In this paper, it was shown that the usual supersymmetric algebra is not valid for supersymmymmetric theories with solitons, and the algebra is modified to include the topological quantum numbers as central charges.
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The Topological Vertex
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