"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.