The Sugawara construction provides a internal action of "rotating the
loop" on loop (vertex) algebras. We describe a uniform approach (joint
with E. Frenkel) to the geometric implications of this construction,
describing the effect on moduli of bundles of variations of the
underlying curve. As an application, we obtain the hamiltonian
picture of isomonodromic deformation and its relation with the KZ
equations and Hitchin system.
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