Non-autonomous Hamiltonian systems related to highest Hitchin integrals
A. Levin, M. Olshanetsky
Abstract
We describe non-autonomous Hamiltonian systems coming from the Hitchin integrable systems. The Hitchin integrals of motion depend on the W-structures of the basic curve. The parameters of the W-structures play the role of times. In particular, the quadratic integrals dependent on the complex structure (W2-structure) of the basic curve and times are coordinate on the Teichmuller space. The corresponding flows are the monodromy preserving equations such as the Schlesinger equations, the Painleve VI equation and their generalizations. The equations corresponding to the highest integrals are monodromy preserving conditions with respect to changing of the Wk-structures (k>2). They are derived by the symplectic reduction from the gauge field theory on the basic curve interacting with Wk-gravity. As by product we obtain the classical Ward identities in this theory.
Create a lesson
Related papers
2-Morita Theory of E2-Algebras and Module Categories
Rongge Xu, Holiverse Yang
Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model
Vincent Rivasseau
Quasi-polynomiality and N-point functions of single connected leaky completed Hurwitz numbers
Chongyu Wang, Chenglang Yang
Coupled stochastic variational principles for multiscale surface gravity waves -- Part I: theoretical framework
Etienne Mémin, Arnaud Debussche
The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
Jiawei He, Xueyin Wang
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu