- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:38
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
47
2011
1
Donaldson = Seiberg–Witten from Mochizuki's Formula and Instanton Counting
Lothar
Göttsche
International Centre for Theoretical Physics, TRIESTE, ITALY
Hiraku
Nakajima
Kyoto University, KYOTO, JAPAN
Kota
Yoshioka
Kobe University, KOBE, JAPAN
Donaldson invariants, Seiberg{Witten invariants, instanton counting
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.
Algebraic geometry
Manifolds and cell complexes
Quantum theory
General
307
359
10.2977/PRIMS/37
http://www.ems-ph.org/doi/10.2977/PRIMS/37