  We present a detailed derivation of the renormalization group equations for
two dimensional electromagnetic Coulomb gases whose charges lie on a triangular
lattice (magnetic charges) and its dual (electric charges). The interactions
between the charges involve both angular couplings and a new electromagnetic
potential. This motivates the denomination of ``elastic'' Coulomb gas. Such
elastic Coulomb gases arise naturally in the study of the continuous melting
transition of two dimensional solids coupled to a substrate, either
commensurate or with quenched disorder.
