We propose an explicit formula connecting Donaldson invariants and Seiberg–Witten invariants of a 4-manifold of simple type via Nekrasov's deformed partition function for the N = 2 SUSY gauge theory with a single fundamental matter. This formula is derived from Mochizuki's formula, which makes sense and was proved when the 4-manifold is complex projective. Assuming our formula is true for a 4-manifold of simple type, we prove Witten's conjecture and sum rules for Seiberg–Witten invariants (superconformal simple type condition), conjectured by Mariño, Moore and Peradze.
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Lothar Göttsche, Hiraku Nakajima, Kota Yoshioka, Donaldson = Seiberg–Witten from Mochizuki's Formula and Instanton Counting. Publ. Res. Inst. Math. Sci. 47 (2011), no. 1, pp. 307–359DOI 10.2977/PRIMS/37