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We consider coarse-graining applied to nonselfintersecting planar center-vortex loops as they emerge in the confining phase of an SU(2) Yang-Mills theory. Well-established properties of planar curve-shrinking predict that a suitably defined, geometric effective action exhibits (mean-field) critical behavior when the conformal limit of circular points is reached. This suggests the existence of an asymptotic mass gap. We demonstrate that the initially sharp mean center-of-mass position in a given ensemble of curves develops a variance under the flow as is the case for a position eigenstate in free-particle quantum mechanics under unitary time evolution. A possible application of these concepts is an approach to high-$T_c$ superconductivity based (a) on the nonlocal nature of the electron (1-fold selfintersecting center-vortex loop) and (b) on planar curve-shrinking flow representing the decrease in thermal noise in a cooling cuprate.
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In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang-Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modelling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the nonoriented center-vortex component and non-Abelian degrees when modelling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.
Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space ${A_mu}$ into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singers theorem on gauge copies only refers to gauge fixing conditions that are global in ${A_mu}$, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.
In this work, we analyzed a recent proposal to detect $SU(N)$ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtained a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we were able to show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first principles, well-defined, and calculable Yang-Mills ensemble.
Maximal t Hooft loops are studied in SO(3) lattice gauge theory at finite temperature T. Tunneling barriers among twist sectors causing loss of ergodicity for local update algorithms are overcome through parallel tempering, enabling us to measure the vortex free energy F and to identify a deconfinement transition at some $beta_A^{crit}$. The behavior of F below $beta_A^{crit}$ shows however striking differences with what is expected from discretizations in the fundamental representation.
A survey for the molecular clouds in the Galaxy with NANTEN mm telescope has discovered molecular loops in the Galactic center region. The loops show monotonic gradients of the line of sight velocity along the loops and the large velocity dispersions towards their foot points. It is suggested that these loops are explained in terms of the buoyant rise of magnetic loops due to the Parker instability. We have carried out global three-dimensional magneto-hydrodynamic simulations of the gas disk in the Galactic center. The gravitational potential is approximated by the axisymmetric potential proposed by Miyamoto & Nagai (1975). At the initial state, we assume a warm (~ 10^4 K) gas torus threaded by azimuthal magnetic fields. Self-gravity and radiative cooling of the gas are ignored. We found that buoyantly rising magnetic loops are formed above the differentially rotating, magnetically turbulent disk. By analyzing the results of global MHD simulations, we have identified individual loops, about 180 in the upper half of the disk, and studied their statistical properties such as their length, width, height, and velocity distributions along the loops. Typical length and height of a loop are 1kpc and 200pc, respectively. The line of sight velocity changes linearly along a loop and shows large dispersions around the foot-points. Numerical results indicate that loops emerge preferentially from the region where magnetic pressure is large. We argue that these properties are consistent with those of the molecular loops discovered by NANTEN.
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