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.