Seiberg-Witten curves and double-elliptic integrable systems

Harry Braden, Gleb Aminov, A. Mironov, A. Morozov, A V Zotov

Research output: Contribution to journalArticlepeer-review


An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.
Original languageEnglish
Article number33
Number of pages14
Journal Journal of High Energy Physics
Publication statusPublished - 9 Jan 2015

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