Self-dual SU(2) invariant Einstein metrics and modular dependence of theta-functions
We simplify Hitchin's description of SU(2)-invariant self-dual Einstein metrics, making use of the tau-function of related four-pole Schlesinger system.
gr-qc↗
arXiv subjects
D. A. Korotkin
Publications and source records attributed to D. A. Korotkin.
On solutions of the Schlesinger Equations in Terms of $Θ$-Functions
In this paper we construct explicit solutions and calculate the corresponding $τ$-function to the system of Schlesinger equations describing isomonodromy deformations of $2\times 2$ matrix linear ordinary differential equation whose coefficients are rational functions with poles of the first order; in particular, in the case when the coefficients have four poles of the first order and the corresponding Schlesinger system reduces to the sixth Painlevé equation with the parameters $1/8, -1/8, 1/8, 3/8$, our construction leads to a new representation of the general solution to this Painlevé equation obtained earlier by K. Okamoto and N. Hitchin, in terms of elliptic theta-functions.
math-ph↗
On the quantization of isomonodromic deformations on the torus
The quantization of isomonodromic deformation of a meromorphic connection on the torus is shown to lead directly to the Knizhnik-Zamolodchikov-Bernard equations in the same way as the problem on the sphere leads to the system of Knizhnik-Zamolodchikov equations. The Poisson bracket required for a Hamiltonian formulation of isomonodromic deformations is naturally induced by the Poisson structure of Chern-Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.
hep-th↗