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Register a new userLattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills
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Authors
Dominik Smith
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We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. Our action includes a kinetic term, the one-loop perturbative potential for the Wilson line, a non-perturbative fuzzy-bag contribution and spatial gauge fields. We determine the phase diagram of the theory and confirm that, at moderately weak coupling, the non-perturbative term leads to eigenvalue repulsion in a finite region above the deconfining phase transition.
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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.
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.
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 calculate the scattering cross section between two $0^{++}$ glueballs in $SU(2)$ Yang-Mills theory on lattice at $beta = 2.1, 2.2, 2.3, 2.4$, and 2.5 using the indirect (HAL QCD) method. We employ the cluster-decomposition error reduction technique and use all space-time symmetries to improve the signal. In the use of the HAL QCD method, the centrifugal force was subtracted to remove the systematic effect due to nonzero angular momenta of lattice discretization. From the extracted interglueball potential we determine the low energy glueball effective theory by matching with the one-glueball exchange process. We then calculate the scattering phase shift, and derive the relation between the interglueball cross section and the scale parameter $Lambda$ as $sigma_{phi phi} = (2 - 51) Lambda^{-2}$ (stat.+sys.). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter, as $Lambda > 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.
We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures close to (and less than) the deconfinement one with the analytical constraints from renormalization-group arguments, from the exact integrability of the two-dimensional Ising model that describes the universality class of the critical point of the theory, from conformal perturbation theory, and from Lorentz invariance, we derive tight quantitative bounds on the corrections to the effective string action beyond the Nambu-Goto approximation. We show that these corrections are compatible with the predictions derived from a bootstrap analysis of the effective string theory, but are inconsistent with the axionic string ansatz.
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