scholarly journals Center vortex properties in the Laplace-center gauge of SU(2) Yang–Mills theory

2001 ◽  
Vol 504 (4) ◽  
pp. 338-344 ◽  
Author(s):  
K. Langfeld ◽  
H. Reinhardt ◽  
A. Schäfke
Keyword(s):  
Yang Mills ◽  
Center Vortex

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

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: modeling 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 non-oriented center-vortex component and non-Abelian degrees of freedom when modeling 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.

scholarly journals Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
H. Reinhardt ◽  
G. Burgio ◽  
D. Campagnari ◽  
E. Ebadati ◽  
J. Heffner ◽  
...  
Keyword(s):  
Spatial Dimension ◽  
String Tension ◽  
Quark Condensate ◽  
Coulomb Gauge ◽  
Hamiltonian Approach ◽  
Critical Temperatures ◽  
Yang Mills ◽  
Center Vortex ◽  
Gauge Fixing ◽  
Deconfinement Phase Transition

We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang–Mills theory, the deconfinement phase transition is found to be second order for SU(2) and first order for SU(3), in agreement with the lattice results. The corresponding critical temperatures are found to be 275 MeV and 280 MeV, respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of 198 MeV and 170 MeV, respectively, for the deconfinement and chiral transition.

scholarly journals Center vortices, area law and the catenary solution

2015 ◽  
Vol 30 (34) ◽  
pp. 1550207 ◽  
Author(s):  
Roman Höllwieser ◽  
Derar Altarawneh
Keyword(s):  
Surface Tension ◽  
Wilson Loop ◽  
Dimensional Model ◽  
Expectation Values ◽  
Yang Mills ◽  
Surface Behavior ◽  
Vortex Lines ◽  
Center Vortex ◽  
Hypercubic Lattice ◽  
Area Law

We present meson–meson (Wilson loop) correlators in Z(2) center vortex models for the infrared sector of Yang–Mills theory, i.e. a hypercubic lattice model of random vortex surfaces and a continuous (2 + 1)-dimensional model of random vortex lines. In particular, we calculate quadratic and circular Wilson loop correlators in the two models, respectively, and observe that their expectation values follow the area law and show string breaking behavior. Further, we calculate the catenary solution for the two cases and try to find indications for minimal surface behavior or string surface tension leading to string constriction.

scholarly journals Center-Vortex Loops with One Self-Intersection

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Julian Moosmann ◽  
Ralf Hofmann
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Noise Level ◽  
Coarse Graining ◽  
Renormalization Group Flow ◽  
Yang Mills ◽  
Vortex Loops ◽  
Center Vortex ◽  
Group Flow ◽  
Ordered State

We investigate the 2D behavior of one-fold self-intersecting, topologically stabilized center-vortex loops in the confining phase of an SU(2) Yang-Mills theory. This coarse-graining is described by curve-shrinking evolution of center-vortex loops immersed in a flat 2D plane driving the renormalization-group flow of an effective “action.” We observe that the system evolves into a highly ordered state at finite noise level, and we speculate that this feature is connected with 2D planar high Tc superconductivity in FeAs systems.

scholarly journals Evolving Center-Vortex Loops

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Julian Moosmann ◽  
Ralf Hofmann
Keyword(s):  
Center Of Mass ◽  
Free Particle ◽  
Mean Field ◽  
Coarse Graining ◽  
Yang Mills ◽  
Vortex Loops ◽  
Center Vortex ◽  
Planar Curve ◽  
Nonlocal Nature ◽  
Mass Position

We consider coarse-graining applied to nonselfintersecting planar centervortex 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- 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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