Nekrasov, Nikita A. Seiberg-Witten prepotential from instanton counting. (English) Zbl 1056.81068 Adv. Theor. Math. Phys. 7, No. 5, 831-864 (2003). 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. Cited in 6 ReviewsCited in 841 Documents 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 PDFBibTeX XMLCite \textit{N. A. Nekrasov}, Adv. Theor. Math. Phys. 7, No. 5, 831--864 (2003; Zbl 1056.81068) Full Text: DOI arXiv