On the Absence of Cross-Confinement for Dynamically Generated   Multi-Chern-Simons Theories
  We show that when the induced parity breaking part of the effective action for the low-momentum region of U(1) x ... x U(1) Maxwell gauge field theory with massive fermions in 3 dimensions is coupled to a \phi^4 scalar field theory, it is not possible to eliminate the screening of the long-range Coulomb interactions and get external charges confined in the broken Higgs phase. This result is valid for non-zero temperature as well. 
Emil M. Prodanov and Siddhartha Sen