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Instanton counting on Hirzebruch surfaces

Le : 28/01/2009 14h35
Par : Ugo BRUZZO (SISSA, Trieste)
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Résumé : We study moduli spaces of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare' polynomial of the latter. We also consider fractional first Chern classes, which means that we are extending our theory to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.