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Register a new userSimulating plasma instabilities in SU(3) gauge theory
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We compute nonequilibrium dynamics of plasma instabilities in classical-statistical lattice gauge theory in 3+1 dimensions. The simulations are done for the first time for the SU(3) gauge group relevant for quantum chromodynamics. We find a qualitatively similar behavior as compared to earlier investigations in SU(2) gauge theory. The characteristic growth rates are about 25 % lower for given energy density, such that the isotropization process is slower. Measured in units of the characteristic screening mass, the primary growth rate is independent of the number of colors.
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We determine the time evolution of fluctuations of the Polyakov loop after a quench into the deconfined phase of SU(3) gauge theory from a simple classical relativistic Lagrangian. We compare the structure factors, which indicate spinodal decomposition followed by relaxation, to those obtained via Markov Chain Monte Carlo techniques in SU(3) lattice gauge theory. We find that the time when the structure factor peaks diverges like $sim 1/k^2$ in the long-wavelength limit. This is due to formation of competing Z(3) domains for configurations where the Polyakov loop exhibits non-perturbatively large variations in space, which delay thermalization of long wavelength modes. For realistic temperatures, and away from the extreme weak-coupling limit, we find that even modes with $k$ on the order of $T$ experience delayed thermalization. Relaxation times of very long wavelength modes are found to be on the order of the size of the system; thus, the dynamics of competing domains should accompany the hydrodynamic description of the deconfined vacuum.
We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition.
A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed temperature are calculated directly on 32^3 x (6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor (T_{mu nu}^R(x)) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t-dependence of the flowed data.
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method local analysis, we conjecture that the conformal region exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred as High Temperature QCD). Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson behave at large t as a power-law corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua and therefore it suggests a first order transition both in Conformal QCD and in High Temperature QCD. Within our fixed lattice simulation, we find that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc respectively. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.
Motivated by recent studies on the resurgence structure of quantum field theories, we numerically study the nonperturbative phenomena of the SU($3$) gauge theory in a weak coupling regime. We find that topological objects with a fractional charge emerge if the theory is regularized by an infrared (IR) cutoff via the twisted boundary conditions. Some configurations with nonzero instanton number are generated as a semi-classical configuration in the Monte Carlo simulation even in the weak coupling regime. Furthermore, some of them consist of multiple fractional-instantons. We also measure the Polyakov loop to investigate the center symmetry and confinement. The fractional-instanton corresponds to a solution linking two of degenerate $mathbb{Z}_3$-broken vacua in the deconfinement phase.
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