  The two-dimensional one-component logarithmic Coulomb gas is mapped onto a
non-hermitian fermionic field theory. At $\beta=2$, the field theory is free.
Correlation functions are calculated and a perturbation theory is discussed for
extending to other $\beta$. A phase transition is found at the mean-field level
at large $\beta$. Some results are extended to spaces of constant negative
curvature.
