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arxiv math/0306198 v2 pith:NZIITW7P submitted 2003-06-12 math.AG hep-thmath-phmath.MP

Instanton counting on blowup. I. 4-dimensional pure gauge theory

classification math.AG hep-thmath-phmath.MP
keywords blowupdeformationequationmathbbmodulinekrasovprepotentialseiberg-witten
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of $\mathbb R^4$, we derive a differential equation for the Nekrasov's partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

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  1. Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean

    hep-th 2026-07 conditional novelty 8.0

    The Seiberg–Witten SU(2) solution is formalized in Lean 4 with physical assumptions as named predicates and mathematical consequences as sorry-free theorems, demonstrating a method for auditing non-rigorous physics arguments.