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

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

2010-01-27

arxiv.org/abs/1001.5024v1

Publ.Res.Inst.Math.Sci.Kyoto 47:307-359,2011

Mathematics

Differential Geometry

43 pages

Scientific paper

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.

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