  We propose that there exist generalized Seiberg-Witten equations in the
Liouville conformal field theory, which allow the computation of correlation
functions from the resolution of certain Ward identities. These identities
involve a multivalued spin one chiral field, which is built from the
stress-energy tensor. We solve the Ward identities perturbatively in an
expansion around the heavy asymptotic limit, and check that the first two terms
of the Liouville three-point function agree with the known result of Dorn,
Otto, Zamolodchikov and Zamolodchikov. We argue that such calculations can be
interpreted in terms of the geometry of non-commutative spectral curves.
