A Framework for Systematic Study of QCD Vacuum Structure II: Coherent Lattice QCD

TL;DR

This paper introduces a unified lattice QCD formulation using a single Dirac operator with exact chiral symmetry, aiming to better understand the QCD vacuum structure through explicit gauge-fermion interrelations.

Contribution

It proposes a novel lattice QCD framework where all elements are derived from the Dirac operator D, enabling new insights into the QCD vacuum structure.

Findings

Proposes a lattice QCD formulation based on the Dirac operator D.

Suggests regularizations where gauge actions are functions of D.

Highlights potential for exploring gauge-fermion interrelations.

Abstract

We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral symmetry. Several regularizations of this type are suggested via constructing scalar densities (gauge actions) that are explicit functions of D. The simplest of these is based on the proposition that classical limit of density associated with Tr D is (up to an additive constant) proportional to FF, while the corresponding operator is local. The possibilities of explicit interrelations between gauge and fermionic aspects of the theory are emphasized together with the utility of such formulations for exploring the QCD vacuum structure.