Lattice study on QCD-like theory with exact center symmetry

Abstract

We investigate QCD-like theory with exact center symmetry, with emphasis on the finite-temperature phase transition concerning center and chiral symmetries. On the lattice, we formulate center symmetric SU(3) gauge theory with three fundamental Wilson quarks by twisting quark boundary conditions in a compact direction (Z 3 -QCD model). We calculate the expectation value of Polyakov loop and the chiral condensate as a function of temperature on 16 3 × 4 and 20 3 × 4 lattices along the line of constant physics realizing m P S /m V = 0.70. We find out the first-order center phase transition, where the hysteresis of the magnitude of Polyakov loop exists depending on thermalization processes. We show that chiral condensate decreases around the critical temperature in a similar way to that of the standard three-flavor QCD, as it has the hysteresis in the same range as that of Polyakov loop. We also show that the flavor symmetry breaking due to the twisted boundary condition gets qualitatively manifest in the high-temperature phase. These results are consistent with the predictions based on the chiral effective model in the literature. Our approach could provide novel insights to the nonperturbative connection between the center and chiral properties.

Instanton-dyon liquid model. V. Twisted light quarks

“…The high temperature phase is center asymmetric with always unequal chiral condensates. Our results are qualitatively consistent with the lattice results reported recently in [20], although with a more pronounced difference between the flavor chiral condensates across the transition region caused mostly by the differences in the leading (twisted) Matsubara modes in the center symmetric phase. In the symmetric ground state we observe the emergence of one massless pion π 0 (2-flavor case).…”

“…A further comparison between the mean field results derived in this paper, with the direct simulations [22] of the instanton-dyon model and lattice results [20], is obviously of great interest.…”

“…The confined phase is both center and chiral symmetric eventhough the boundary conditions are flavor breaking. The deconfined phase is center and chiral symmetry broken [19,20].…”

Interplay between sign problem andZ3symmetry in three-dimensional Potts models

“…In the papers, the phase structure in the Z 3 -QCD was studied by using the Polyakov-loop extended NambuJona-Lasinio (PNJL) model [28][29][30][31][32] as an effective model of QCD. Recently, lattice simulations of Z 3 -QCD was done at µ = 0 [33]. The result was shown to be consistent with the PNJL-model prediction.…”

QCD on a small circle

“…[44] (see also Refs. [45][46][47][48][49][50][51][52][53]). To preserve reflection (in the compactified direction) and charge conjugation symmetries, we also require that complex conjugation leave this set of eigenvalues unchanged.…”