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We consider the generating functional (logarithm of the normalization factor)of the Laughlin state on a sphere, in the limit of a large number of particles$N$. The problem is reformulated in terms of a perturbative expansion of a 2dQFT, resembling the Liouville field theory. We develop an analog of theLiouville loop perturbation theory, which allows us to quantitatively study thegenerating functional for an arbitrary smooth metric and an inhomogeneousmagnetic field beyond the leading orders in large $N$.

Liouville perturbation theory for Laughlin state and Coulomb gas