Massive Quantum Vortex Excitations in a Pure Gauge Abelian Theory in 2 + 1D

We introduce and study a pure gauge Abelian theory in 2 + 1D in which massive quantum vortex states do exist in the spectrum of excitations. This theory can be mapped in a three-dimensional gas of point particles with a logarithmic interaction, in the grand-canonical ensemble. We claim that this theory is the 2 + 1D analog of the sine–Gordon, the massive vortices being the counterparts of sine–Gordon solitons. We show that a symmetry breaking, order parameter, similar to the vacuum expectation value of a Higgs field does exist.