We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.
We study the frequency dependencies in the renormalization of the fermion Green's function for the $\ensuremath{\pi}$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region, we self-consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency-dependent Lindhard screening and retardation effects.
Institut fur Kernphysik, Technische Universitat Darmstadt, D-64289 Darmstadt, GermanyE-mail: nstrodt@crunch.ikp.physik.tu-darmstadt.deWe study center vortex free energies and ’t Hooft’s electric fluxes on the lattice in 2+1 dimen-sions, where SU(2) for example, is in the universality class of the 2d Ising model. This placesa wealth of exact results at our fingertips. In particular, spacelike center vortices in SU(2) nearcriticality correspond to spin interfaces in the 2d Ising model, whose universal scaling functionsare known exactly. We exploit this to locate the deconfinement transition with unprecedentedprecision and subsequently for a finite size scaling analysis, where the self-duality of the 2d spinmodel is reflected in a duality between the spacelike vortices and confining electric fluxes. Thecorresponding relation between the string tension and its dual in the high temperature phase isarguably the simplest example of a universal amplitude ratio. Around the transition, both can beefficiently extracted from the exact results with a global one-parameter fit which allows straight-forward continuum extrapolation.The XXVIII International Symposium on Lattice Field Theory, Lattice2010June 14-19, 2010Villasimius, Sardinia, Italy
We illustrate in a simple toy model how the methods of SUSY quantum mechanics and topological quantum field theory can be used for covariant gauge-fixing with unbroken BRST symmetry on a finite lattice.
We summarize results on finite-volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. We demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. We discuss the relation of our solutions with results from lattice Monte-Carlo simulations.
Also cited as: Lattice 2007, the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany / Gunnar Bali, Vladimir Braun, Christof Gattringer, Meinulf Gockeler, Andreas Schafer, Peter Weisz, Tilo Wettig (eds.): pp. 340/1-340/7.
We study fermionic excitations in a hot and dense strongly interacting medium consisting of quarks and (pseudo-)scalar mesons. In particular, we use the two-flavor quark-meson model in combination with the functional renormalization group (FRG) approach, which allows to take into account the effects from thermal and quantum fluctuations. The resulting fermionic excitation spectrum is investigated by calculating the quark spectral function at finite temperature, quark chemical potential, and spatial momentum. This involves an analytic continuation from imaginary to real energies by extending the previously introduced analytically continued FRG method to the present case. We identify three different collective excitations in the medium: the ordinary thermal quark, the plasmino mode, and an ultrasoft ``phonino'' mode. The dispersion relations of these modes are extracted from the quark spectral function. When compared to corresponding results from an FRG-improved one-loop calculation, a remarkable agreement has been found.
We give an update on our lattice determination of r 0 Λ MS for different N f .Our calculations employ the strong coupling constant in the minimal MOM scheme for QCD in Landau gauge, and we report here on our progress towards a quantitative understanding of the intrinsic lattice discretization artifacts at large momenta.This is important for a high-precision analysis, in particular for the unquenched calculations for which the access to small lattice spacings is restricted by the available gauge configurations.
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