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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.

We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic c-function (C(l)) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For 0 l 0.7 fm, where l is the length of the subspace, the entropic c-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20 % discrepancy. When l is close to the Hadronic scale, the entropic c-function decreases smoothly, and it is consistent with zero within error bars at l 0.9 fm.Quantum entanglement is a fascinating phenomenon that was first highlighted by the Einstein-Podolsky-Rosen paradox [1] and has remained a focus of research activity for decades. If there is a system in a pure quantum state, measurements on a subsystem A determine the results of measurements on its complement B, even if no causal communication is possible between the two measurements. The entanglement entropy S A of subsystem A is defined as von Neumann entropy corresponding to the reduced density matrix ρ A :where ρ A = Tr HB [ρ tot ], and it is assumed that the total Hilbert space is a direct product of two subspaces corresponding to the subsystems considered, H tot = H A ⊗H B . More generally, studies of the entanglement entropy become central in cases of complex systems with strong interactions, where the properties of the ground state cannot be evaluated directly. In particular, the notion of quantum entanglement is crucial for the theory of quantum phase transitions, i.e., non-thermal phase transitions at temperature T = 0 [2][3][4]. In physics of black holes, consideration of the quantum entanglement is central to discussions of the information paradox [5], which challenges the consistency of general relativity and quantum mechanics.Applications to field theory are more recent. First of all, the entanglement entropy is ultraviolet divergent in field theory [6]. In more detail, one considers the vacuum state and defines the subsystem A as a slab of length l in one of the spatial dimensions, at a fixed time slice. Then, the entanglement entropy contains, as its most divergent term, a term that is proportional to |∂A|/a d−1 , where d is the number of spatial dimensions, a is the lattice spacing, and |∂A| is the area of the boundary surface between the slab and the rest of the space. To eliminate this divergence, which depends on details of the UV cutoff, one focuses on the entropic c-function [7]:

We delineate equilibrium phase structure and topological charge distribution of dense two-colour QCD at low temperature by using a lattice simulation with two-flavour Wilson fermions that has a chemical potential µ and a diquark source j incorporated. We systematically measure the diquark condensate, the Polyakov loop, the quark number density and the chiral condensate with improved accuracy and j → 0 extrapolation over earlier publications; the known qualitative features of the low temperature phase diagram, which is composed of the hadronic, Bose-Einstein condensed (BEC) and BCS phases, are reproduced. In addition, we newly find that around the boundary between the hadronic and BEC phases, nonzero quark number density occurs even in the hadronic phase in contrast to the prediction of the chiral perturbation theory (ChPT), while the diquark condensate approaches zero in a manner that is consistent with the ChPT prediction. At the highest µ, which is of order the inverse of the lattice spacing, all the above observables change drastically, which implies a lattice artifact. Finally, at temperature of order 0.45T c , where T c is the chiral transition temperature at zero chemical potential, the topological susceptibility is calculated from a gradient-flow method and found to be almost constant for all the values of µ ranging from the hadronic to BCS phase. This is a contrast to the case of 0.89T c in which the topological susceptibility becomes small as the hadronic phase changes into the quark-gluon plasma phase.

A parametrization of the lattice spacing (a) in terms of the bare coupling (β) for the SU(3) Yang-Mills theory with the Wilson gauge action is given in a wide range of β. The Yang-Mills gradient flow with respect to the flow time t for the dimensionless observable, t d dt t 2 E(t) , is utilized to determine the parametrization. With fine lattice spacings (6.3 ≤ β ≤ 7.5) and large lattice volumes (N s = 64-128), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error.

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We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations. * ) Here we take the continuum limit and estimate the systematic error in the same way as we did in subsection 4.3.