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Register a new userFractional instanton of the SU($3$) gauge theory in weak coupling regime
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Authors
Etsuko Itou
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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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According to recent studies on resurgence scenario of quantum systems, some topological objects with fractional charges play an important role to see the resurgence structure. In this talk, we report a numerical evidence of the fractional-instantons of the SU($3$) gauge theory. The fractional-instanton appears in a weak coupling regime, if the theory is regularized by an infrared (IR) cutoff via the $1$-form twisted boundary conditions. The Polyakov loop is also measured 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. This talk is based on the paper[1].
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.
Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory. Unlike previous studies, we focus on back reaction on the holonomy and the issue of confinement. We calculate the free energy as a function of the holonomy and the dyon densities, using standard Metropolis Monte Carlo and integration over parameter methods. We observe that as the temperature decreases and the dyon density grows, its minimum indeed moves from small holonomy to the value corresponding to confinement. We then report various parameters of the self-consistent ensembles as a function of temperature, and investigate the role of inter-particle correlations.
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.
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