Theory of Light Quarks in the Confining Vacuum

TL;DR

This paper investigates how light quarks propagate in a confining vacuum, demonstrating the scalar nature of confinement and its link to chiral symmetry breaking using gauge-invariant correlators and the relativistic WKB method.

Contribution

It provides a detailed theoretical analysis of light quark confinement and chiral symmetry breaking through gauge-invariant correlators and nonlinear equations in the large $N_c$ limit.

Findings

Scalar confining interaction for light quarks confirmed

Chiral condensate estimated using WKB method

Connection between confinement and chiral symmetry breaking established

Abstract

The light quark propagation in the confining vacuum, described by an (infinite) set of gauge-invariant vacuum correlators, is studied in detail. To keep gauge invariance at each step the system of light quark and heavy antiquark is considered, and the nonlinear equations are written explicitly for the quark propagator in the limit of large $N_c$. For the lowest (Gaussian) correlator the system is studied in various approximations, and the relativistic WKB method is used to demonstrate the scalar confining interaction of light quarks, which implies chiral symmetry breaking. The chiral condensate is estimated by the relativistic WKB method, and connection to the density of global zero modes is clarified. The higher even order correlators are shown to yield the same properties of scalar confining interaction for light quarks. No attempt was made to solve the obtained nonlinear equations numerically, but the qualitative conclusion on connection between confinement and chiral symmetry breaking is drawn, and an estimate of the chiral condensate is performed.