Anomalous quantum Hall effect of 4D lattice QCD in background fields

Borici-Creutz (BC) model describing the dynamics of light quarks in lattice QCD has been shown to be intimately linked to the four dimensional extension of 2D graphene refereed below to as four dimensional graphene (4D-graphene). Borrowing ideas from the field theory description of the usual 2D graphene, we study in this paper the anomalous quantum Hall effect (AQHE) of the BC fermions in presence of a constant background field strength F-mu v with a special focuss on the case F-mu v = B epsilon(mu v34) + E epsilon(12 mu v) with B and e two real moduli and det F-mu v - B(2)xE(2). First, we revisit the anomalous 2D graphene by using OFT method. Then, we consider the AQHE of BC fermions for both regular det F-mu v not equal 0 and singular det F-mu v = 0 cases. We show, amongst others, that the exact solutions of the BC fermions coupled to constant F-mu v have a 5D interpretation; and the filling factor v(BC) of the BC model coupled to onstant F-mu v is given by 24(2N+1)(2M+1)/2 with N, M positive integers. Others features, such as F-mu v(QCD) not equal 0 and the extension of the obtained results to the lattice fermions like Karsten-Wilzeck (KW) fermions and naive ones, are also discussed.