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Donaldson = Seiberg–Witten from Mochizuki's Formula and Instanton Counting

2011; Kyoto University; Volume: 47; Issue: 1 Linguagem: Inglês

10.2977/prims/37

1663-4926

Lothar Göttsche, Hiraku Nakajima, Kōta Yoshioka,

Algebraic structures and combinatorial models

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.