Baptiste Filoche - Wall-crossing of Instantons on the Blow-up
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Abstract: Instanton partition functions provide an exact framework for computing non-perturbative corrections to the Seiberg–Witten prepotential in four-dimensional supersymmetric gauge theories. Two key developments leading to the instanton partition function are Nekrasov’s localization formalism, and the recursive Nakajima–Yoshioka blow-up formula, which relates the instanton partition function on the blow-up of C^2 to the one on flat space. In this presentation, I will review these results and discuss wall-crossing phenomena arising from different stability conditions in the instanton moduli space on the blow-up. Using a contour-integral formulation based on the Jeffrey–Kirwan residue prescription, the chamber dependence of the partition function can be characterized in terms of bipartite graphs and super-partitions. This formalism can then be used to provide an alternative derivation of the blow-up formula. This presentation is based on [2604.20674] in collaboration with Stefan Hohenegger and Taro Kimura.
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