Effective field theory of the classical two-dimensional plasma

Using techniques of effective field theory, we consider the thermodynamical properties of a dilute two-dimensional plasma interacting via a $1/r$ potential. The first one-loop correction to the partition function is already logarithmically divergent in the effective theory. The finite part of the one-loop induced couplings is then explicitly evaluated by matching the density-density correlator in the effective theory and in the full quantum theory. This task is performed from the formulation of the Coulomb problem in momentum space by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. We also report some higher order results that, in the case of the one-component plasma immersed in a uniform neutralizing background, are resummed to obtain the complete leading-log partition function.