English

Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting

Differential Geometry 2011-08-04 v1 High Energy Physics - Theory Algebraic Geometry

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 Mari\~no, Moore and Peradze.

Keywords

Cite

@article{arxiv.1001.5024,
  title  = {Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting},
  author = {Lothar Göttsche and Hiraku Nakajima and Kota Yoshioka},
  journal= {arXiv preprint arXiv:1001.5024},
  year   = {2011}
}

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43 pages