We describe the methods used to calculate the nucleon structure functions from quenched lattice QCD, and present some results for moments of the polarized and unpolarized structure functions.

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We study the Abelian projected SU(2) lattice gauge theory after gauge fixing to the maximally Abelian gauge (MAG). In order to check the universality of the Abelian dominance we employ the tadpole improved tree level (TI) action. We show that the density of monopoles in the largest cluster (the IR component) is finite in the continuum limit which is approximated already at relatively large lattice spacing. The value itself is smaller than in the case of Wilson action. We present results for the ratio of the Abelian to non-Abelian string tension for both Wilson and TI actions for a number of lattice spacings in the range 0.06 fm < a < 0.35 fm. These results show that the ratio is between 0.9 and 0.95 for all considered values of lattice couplings and both actions. We compare the properties of the monopole clusters in two gauges -in MAG and in the Laplacian Abelian gauge (LAG). Whereas in MAG the infrared component of the monopole density shows a good convergence to the continuum limit, we find that in LAG it is even not clear whether a finite limit exists.

The string tensions of flux tubes associated with static charges in various SU(3) representations are studied within the dual Ginzburg-Landau (DGL) theory. The ratios of the string tensions between higher and fundamental representations, $d_{D} \equiv \sigma_{D}/\sigma_{F}$, are found to depend only on the Ginzburg-Landau (GL) parameter, $\kappa = m_{\chi}/m_{B}$, the mass ratio between monopoles $m_\chi$ and dual gauge bosons $m_B$. In the case of the Bogomol'nyi limit ($\kappa=1$), analytical values of $d_{D}$ are easily obtained by adopting the manifestly Weyl invariant formulation of the DGL theory, which are provided simply by the number of color-electric Dirac strings inside the flux tube. A numerical investigation of the ratio for various GL-parameter cases is also performed, which suggests that the Casimir scaling is obtained in the type-II parameter range within the interval $\kappa=5 \sim 9$ for various ratios $d_D$.Comment: 14 pages, 3 eps figures, RevTex. The version accepted for publication in Phys.Rev.D (Rapid Communications