We propose that there exist Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. Such identities involve a multivalued spin one current, which is related to the stress-energy tensor. We expand the Ward identities around the heavy asymptotic limit, and express their solution in terms of the geometry of a non-commutative spectral curve. We thus compute the first two terms of the three-point function in this expansion, and check that they agree with already known results.