Mathematics – Algebraic Geometry
Scientific paper
2004-09-22
Mathematics
Algebraic Geometry
16 pages; to appear in a special volume dedicated to A.Joseph's 60th birthday
Scientific paper
We 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.
Braverman Alexander
Etingof Pavel
No associations
LandOfFree
Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-77796