2013/11/15 by Hideo Suganuma, Takahiro M. Doi, Takumi Iritani · 2 citations
Physics and Astronomy · #hep-lat #hep-ph #hep-th
published as PoS LATTICE2013 (2013) 374 · Proc. of LATTICE2013
arxiv created 2013/11/15 · arxiv updated 2013/11/18
We derive an analytical gauge-invariant relation between the Polyakov loop ⟨ LP ⟩ and the Dirac eigenvalues λn in QCD, i.e., ⟨ LP ⟩ ∝ ∑n λnNt -1 ⟨ n| U4|n ⟩, on a temporally odd-number lattice, where the temporal lattice size Nt is odd. Here, we use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for link-variables in the temporal direction. This relation is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes |n⟩. Because of the factor λnNt -1 in the Dirac spectral sum, this analytical relation indicates negligibly small contribution of low-lying Dirac modes to the Polyakov loop in both confined and deconfined phases, while the low-lying Dirac modes are essential for chiral symmetry breaking. Also, we numerically confirm the analytical relation, non-zero finiteness of ⟨ n| U4|n ⟩, and tiny contribution of low-lying Dirac modes to the Polyakov loop in lattice QCD simulations. Thus, we conclude that low-lying Dirac modes are not essential modes for confinement, and there is no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD.