Phase structure of non-compact QED3 and the Abelian Higgs model

We review the phase structure of a three-dimensional, non-compact Abelian gauge theory (QED3) as a function of the number N of 4-component massless fermions. There is a critical N-c up to which there is dynamical fermion mass generation and an associated global symmetry breaking. We discuss various approaches to the determination of N-c, which lead to estimates ranging from N-c = 1 to N-c = 4. This theory with N = 2 has been employed as an effective continuum theory for the 2D quantum antiferromagnet where the observed Neel ordering corresponds to dynamical fermion mass generation. Thus the value of N-c is of some physical interest. We also consider the phase structure of the model with a finite gauge boson mass (the Abelian Higgs model).