JournalsprimsVol. 47, No. 1pp. 307–359

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

  • Lothar Göttsche

    International Centre for Theoretical Physics, Trieste, Italy
  • Hiraku Nakajima

    Kyoto University, Japan
  • Kota Yoshioka

    Kobe University, Japan
Donaldson = Seiberg–Witten from Mochizuki's Formula and Instanton Counting cover
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Abstract

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.

Cite this article

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. 307–359

DOI 10.2977/PRIMS/37