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Seiberg-Witten prepotential from instanton counting. (English) Zbl 1056.81068

Summary: Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [A. Losev, N. A. Nekrasov, S. Shatashvili, Nucl. Phys. B 543, No. 3, 549–611 (1998; Zbl 0954.57013)]. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the \(M\)-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.

MSC:

81T45 Topological field theories in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
57R56 Topological quantum field theories (aspects of differential topology)
57R57 Applications of global analysis to structures on manifolds
14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)

Citations:

Zbl 0954.57013
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