We study the four-fermion theory with the ${\mathrm{CP}}^1$ model in 2+1 dimensions. The low-energy effective action is derived and the low-lying spectrum of the model is obtained. Through the Landau-Ginzburg description, it is shown that, for the superconducting case, the model is identical to the anyonic superconductivity model.

• Received 15 April 1993

DOI:https://doi.org/10.1103/PhysRevD.48.2949