Knot Topology of QCD Vacuum

We show that one can express the knot equation of Skyrme theory completely in terms of the vacuum potential of SU(2) QCD, in such a way that the equation is viewed as a generalized Lorentz gauge condition which selects one vacuum for each class of topologically equivalent vacua. From this we show that there are three ways to describe the QCD vacuum (and thus the knot), by a non-linear sigma field, a complex vector field, or by an Abelian gauge potential. This tells that the QCD vacuum can be classified by an Abelian gauge potential with an Abelian Chern-Simon index.Comment: 4 page

Chromoelectric Knot in QCD

We argue that the Skyrme theory describes the chromomagnetic (not chromoelectric) dynamics of QCD. This shows that the Skyrme theory could more properly be interpreted as an effective theory which is dual to QCD, rather than an effective theory of QCD itself. This leads us to predict the existence of a new type of topological knot, a twisted chromoelectric flux ring, in QCD which is dual to the chromomagnetic Faddeev-Niemi knot in Skyrme theory. We estimate the mass and the decay width of the lightest chromoelectric knot to be around $50 GeV$ and $117 MeV$.Comment: 4 page

Non-locality of Hydrodynamic and Magnetohydrodynamic Turbulence

We compare non-locality of interactions between different scales in hydrodynamic (HD) turbulence and magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium. We use 3-dimensional incompressible direct numerical simulations to evaluate non-locality of interactions. Our results show that non-locality in MHD turbulence is much more pronounced than that in HD turbulence. Roughly speaking, non-local interactions count for more than 10\% of total interactions in our MHD simulation on a grid of $512^3$ points. However, there is no evidence that non-local interactions are important in our HD simulation with the same numerical resolution. We briefly discuss how non-locality affects energy spectrum.Comment: 6 pages, 5 figure

Non-Abrikosov Vortex and Topological Knot in Two-gap Superconductor

We establish the existence of topologically stable knot in two-gap superconductor whose topology $\pi_3(S^2)$ is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in Ginzburg-Landau theory of two-gap superconductor which has a non-vanishing condensate at the core, and identify the knot as a twisted magnetic vortex ring made of the helical vortex. We discuss how the knot can be constructed in the recent two-gap $\rm MgB_2$ superconductor.Comment: 4 pages, 3 figure