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Register a new userString-like behaviour of 4d SU(3) Yang-Mills flux tubes
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N.D. Hari Dass
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We present here results on the fine structure of the static qbar q potential in d=4 SU(3) Yang-Mills theory. The potential is obtained from Polyakov loop correlators having separations between 0.3 and 1.2 fermi. Measurements were carried out on lattices of spatial extents of about 4 and 5.4 fermi. The temporal extent was 5.4 fermi in both cases. The results are analyzed in terms of the force between a qbar q pair as well as in terms of a scaled second derivative of the potential. The data is accurate enough to distinguish between different effective string models and it seems to favour the expression for ground state energy of a Nambu-Goto string.
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By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in Landau gauge) in the low momentum regime and to give rise to an OPE correction to the latter of ${sqrt{sigma}}/{p^3}$.The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistent with the vortex picture. Finally, the ghost propagator of maximal center gauge is found to be infrared finite and thus shows that the coset fields play no role for confinement.
An attempt to adapt the study of color flux tubes to the case of finite temperature has been made. The field is measured both through the correlator of two Polyakov loops, one of which connected to a plaquette, and through a connected correlator of Wilson loop and plaquette in the spatial sublattice. Still the profile of the flux tube resembles the transverse field distribution around an isolated vortex in an ordinary superconductor. The temperature dependence of all the parameters characterizing the flux tube is investigated.
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.
The center vortex model for the infrared sector of SU(3) Yang-Mills theory is reviewed. After discussing the physical foundations underlying the model, some technical aspects of its realisation are discussed. The confining properties of the model are presented in some detail and compared to known results from full lattice Yang-Mills theory. Particular emphasis is put on the new phenomenon of vortex branching, which is instrumental in establishing first order behaviour of the SU(3) phase transition. Finally, the vortex free energy is verified to furnish an order parameter for the deconfinement phase transition. It is shown to exhibit a weak discontinuity at the critical temperature, in agreement with predictions from lattice gauge theory.
We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48^4 and three values of the inverse coupling, beta=5.8, 6.0 and 6.2. While finite-volume effects are hardly visible in the effective Coulomb potential, scaling violations and a strong dependence on the choice of Gribov copy are observed. We obtain bounds for the Coulomb string tension that are in agreement with Zwanzigers inequality relating the Coulomb string tension to the Wilson string tension.
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