Relation between Confinement and Chiral Symmetry Breaking in Temporally Odd-number Lattice QCD

Understand

In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking.

• A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition for link-variables.
• This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and it is numerically confirmed at the quenched level in both confinement and deconfinement phases.
• This fact indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD.