Relating Quark Confinement and Chiral Symmetry Breaking in QCD

Understand

We study the relation between quark confinement and chiral symmetry breaking in QCD.

• Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes.
• In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $\lambda_n$ such as $\lambda_n^{N_t-1}$, which behaves as a reduction factor for small $\lambda_n$.
• Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities,while they are essential for chiral symmetry breaking.