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Register a new userOn the color structure of Yang-Mills theory with static sources in a periodic box
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We present an exploratory numerical study on the lattice of the color structure of the wave functionals of the SU(3) Yang-Mills theory in the presence of a $qbar q$ static pair. In a spatial box with periodic boundary conditions we discuss the fact that all states contributing to the Feynman propagation kernel are global color singlets. We confirm this numerically by computing the correlations of gauge-fixed Polyakov lines with color-twisted boundary conditions in the time direction. The values of the lowest energies in the color singlet and octet external source sectors agree within statistical errors, confirming that both channels contribute to the lowest (global singlet) state of the Feynman kernel. We then study the case of homogeneous boundary conditions in the time direction for which the gauge-fixing is not needed. In this case the lowest energies extracted in the singlet external source sector agree with those determined with periodic boundary conditions, while in the octet sector the correlator is compatible with being null within our statistical errors. Therefore consistently only the singlet external source contribution has a non-vanishing overlap with the null-field wave functional.
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We report about an ongoing lattice field theory project concerned with the investigation of heavy hybrid mesons. In particular we discuss our computation of the structure of hybrid static potential flux tubes in SU(2) lattice Yang-Mills theory, which is based on the squares of the chromoelectric and chromomagnetic field strength components. Our flux tube results for hybrid static potential quantum numbers $Sigma_g^-$, $Sigma_u^+$, $Sigma_u^-$, $Pi_g$, $Pi_u$, $Delta_g$, $Delta_u$ are significantly different compared to the flux tube of the ordinary static potential.
Color confinement is the most puzzling phenomenon in the theory of strong interaction based on a quantum SU(3) Yang-Mills theory. The origin of color confinement supposed to be intimately related to non-perturbative features of the non-Abelian gauge theory, and touches very foundations of the theory. We revise basic concepts underlying QCD concentrating mainly on concepts of gluons and quarks and color structure of quantum states. Our main idea is that a Weyl symmetry is the only color symmetry which determines all color attributes of quantum states and physical observables. We construct an ansatz for classical Weyl symmetric dynamical solutions in SU(3) Yang-Mills theory which describe one particle color singlet quantum states for gluons and quarks. Abelian Weyl symmetric solutions provide microscopic structure of a color invariant vacuum and vacuum gluon condensates. This resolves a problem of existence of a gauge invariant and stable vacuum in QCD. Generalization of our consideration to SU(N) (N=4,5) Yang-Mills theory implies that the color confinement phase is possible only in SU(3) Yang-Mills theory.
We consider two fundamental long-standing problems in quantum chromodynamics (QCD): the origin of color confinement and structure of a true vacuum and color singlet quantum states. There is a common belief that resolution to these problems needs a knowledge of a strict non-perturbative quantum Yang-Mills theory and new ideas. Our principal idea in resolving these problems is that structure of color confinement and color singlet quantum states must be determined by a Weyl symmetry which is an intrinsic symmetry of the Yang-Mills gauge theory, and by properties of a selected class of solutions satisfying special requirements. Following this idea we construct for the first time a space of color singlet one particle quantum states for primary gluons and quarks and reveal the structure of color confinement in quantum Yang-Mills theory. As an application we demonstrate formation of physical observables in a pure QCD, pure glueballs.
Results of a numerical simulation concerning the low-lying spectrum of four-dimensional N=1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos are reported. We use the tree-level Symanzik improved gauge action and Wilson fermions with stout smearing of the gauge links in the Wilson-Dirac operator. The configurations are produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed simulations on lattices up to a size of 24^3x48 at beta=1.6. Using QCD units with the Sommer scale being set to r_0=0.5 fm, the lattice spacing is about a~0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to control finite size effects. At the lightest simulated gluino mass our results indicate a mass for the lightest gluino-glue bound state, which is considerably heavier than the values obtained for its possible superpartners. Whether supermultiplets are formed remains to be studied in upcoming simulations.
Energy momentum tensor (EMT) characterizes the response of the vacuum as well as the thermal medium under the color electromagnetic fields. We define the EMT by means of the gradient flow formalism and study its spatial distribution around a static quark in the deconfined phase of SU(3) Yang-Mills theory on the lattice. Although no significant difference can be seen between the EMT distributions in the radial and transverse directions except for the sign, the temporal component is substantially different from the spatial ones near the critical temperature $T_c$. This is in contrast to the prediction of the leading-order thermal perturbation theory. The lattice data of the EMT distribution also indicate the thermal screening at long distance and the perturbative behavior at short distance.
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