Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential

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dc.creatorBraverman, Alexander
dc.creatorEtingof, Pavel
dc.date2004-09-22
dc.date2005-11-05
dc.date.accessioned2026-07-07T06:38:50Z
dc.date.available2026-07-07T06:38:50Z
dc.descriptionWe introduce the notion of the (instanton part of the) Seiberg-Witten prepotential for general Schrodinger operators with periodic potential. In the case when the operator in question is integrable we show how to compute the prepotential in terms of period integrals; this implies that in the integrable case our definition of the prepotential coincides with the one that has been extensively studied in both mathematical and physical literature. As an application we give a proof of Nekrasov's conjecture connecting certain "instanton counting" partition function for an arbitrary simple group G with the prepotential of the Toda integrable system associated with the affine Lie algebra whose affine Dynkin diagram is dual to that of the affinization of the Lie algebra of G (for G=SL(n) this conjecture was proved earlier in the works of Nekrasov-Okounkov and Nakajima-Yoshioka). Our proof is totally different and it is based on the results of the paper math.AG/0401409 by the first author.
dc.description16 pages; to appear in a special volume dedicated to A.Joseph's 60th birthday
dc.identifierhttps://arxiv.org/abs/math/0409441
dc.identifierhttp://arxiv.org/abs/math/0409441
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100877
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject14J60; 14J80
dc.titleInstanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential
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