Coherent lattice QCD

We discuss a proposal for the construction of lattice QCD with gauge action, fermionic action, theta-term, and the operators all based on the lattice Dirac operator D with exact chiral symmetry. The simplest regularization of this type uses the proposition that the classical limit of scalar gauge density associated with trace of D is (up to an additive constant) proportional to tr(FF), while the corresponding operator is local. More general formulations from this class are considered with the aim of exposing interrelations between gauge and fermionic aspects of QCD which are otherwise hidden in generic formulations. Possible utility of these formulations for exploring QCD vacuum structure is emphasized.