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Register a new userAsymptotic freedom and quarks confinement treated through Thompsons approach
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In this work, we first use Thompsons renormalization group method to treat QCD-vacuum behavior close to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a paramagnetic system of a classical theory in the sense that virtual color charges (gluons) emerge in it as spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Making a classical analogy with the paramagnetism of Landaus theory,we are able to introduce a kind of Landau effective action without temperature and phase transition for simply representing QCD-vacuum behavior at higher energies as magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning allows us to use Thompsons heuristic approach in order to extract an effective susceptibility ($chi>0$) of QCD-vacuum. It depends on logarithmic of energy scale u to investigate hadronic matter. Consequently,we are able to get an effective magnetic permeability ($mu>1$) of such a paramagnetic vacuum. As QCD-vacuum must obey Lorentz invariance,the attainment of $mu>1$ must simply require that the effective electrical permissivity is $epsilon<1$,in such a way that $muepsilon=1$ (c^2=1).This leads to the antiscreening effect, where the asymptotic freedom takes place. On the other hand, quarks cofinement, a subject which is not treatable by perturbative calculations, is worked by the present approach. We apply the method to study this subject in order to obtain the string constant, which is in agreement with the experiments.
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An effective field theory model of the massive Yang-Mills theory is considered. Assuming that the renormalized coupling constants of non-renormalizable interactions are suppressed by a large scale parameter it is shown that in analogy to the non-abelian gauge invariant theory the dimensionless coupling constant vanishes logarithmically for large values of the renormalization scale parameter.
We provide strong evidence that the asymptotically free (1+1)-dimensional non-linear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the Heisenberg-comb, that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg-comb consists of a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of time-evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.
We study four-dimensional gauge theories coupled to fermions in the fundamental and meson-like scalars. All requisite beta functions are provided for general gauge group and fermion representation. In the regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up to three loop in the gauge and two loop in the Yukawa and quartic couplings. We find that the conformal window of ultraviolet fixed points is narrowed-down by finite-$N$ corrections beyond the Veneziano limit. We also find a new infrared fixed point whose main features such as scaling exponents, UV-IR connecting trajectories, and phase diagram are provided. Both fixed points collide upon varying the number of fermion flavours $N_{rm f}$, and conformality is lost through a saddle-node bifurcation. We further revisit the prospect for ultraviolet fixed points in the large $N_{rm f}$ limit where matter field fluctuations dominate. Unlike at weak coupling, we do not find clear evidence for new scaling solutions even in the presence of scalar and Yukawa couplings.
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