Confinement and quantum anomaly in quasi-1D spinless fermion chains

We consider the field renormalization group (RG) of two coupled one-spatial dimension (1D) spinless fermion chains under intraforward, interforward, interbackscattering and interumklapp interactions until two-loops order. Up to this order, we demonstrate the quantum confinement in the RG flow, where the interband chiral Fermi points reduce to single chiral Fermi points and the renormalized interaction couplings have Luttinger liquid fixed points. We show that this quasi-1D system is equivalently described in terms of one and two-color interactions and address the problem of quantum anomaly, inherent to this system, as a direct consequence of coupling 1+1 free Dirac fields to one and two-color interactions.