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Kurt Langfeld

Publications and source records attributed to Kurt Langfeld.

At least 73 records · Page 4Linked to original sources
arXiv2003

Vortex critical behavior at the de-confinement phase transition

The de-confinement phase transition in SU(2) Yang-Mills theory is revisited in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axis are studied. Using the percolation cumulant, the temperature for the percolation transition is seen to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.

hep-lat↗
arXiv2003

The Gribov problem and its solution from a toy model point of view

The standard Faddeev Popov gauge fixing procedure is put on solid grounds by taking into account a topological factor which corrects for the number of Gribov copies within the first Gribov horizon. Zwanziger's stochastic approach to gauge fixed Yang-Mills theory is briefly reviewed. A simple toy model is presented which illustrates both methods. Within the toy model, I show that a stochastic drift force can be constructed with which the gauged configurations are attracted by the fundamental modular region. The toy model shows that an action which gives rise to the drift force can be found. This makes a ``heat bath'' simulation possible, which is seen to be superior to the Langevin approach at the numerical level.

hep-lat↗
arXiv2002

Lattice effective theory and the phase transition at finite densities

The transition from the hadronic phase to the phase of color-superconductivity at large densities is addressed by an effective theory which incorporates the Yang-Mills dynamics in addition to the di-quark degree of freedom. A toy version of this theory is studied by lattice simulations. A first order phase transition separates the regime of broken color-electric flux tubes from the color superconducting phase. My findings suggest that the quark and gluon liberation occurs at the same critical chemical potential.

hep-lat↗
arXiv2002

On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory

Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2) lattice gauge theory defines closed trajectories of magnetic monopoles. These trajectories can be interpreted in terms of an effective scalar field theory of the MAG monopoles using the worldline representation of the functional determinants. Employing the monopole worldlines detected in the numerical simulation, we show that a scalar bound state exists. The screening mass $m$ of this state properly scales towards the continuum limit. We find m ~ 1.3 $GeV when the string tension sigma = 440 MeV is used as reference scale.

hep-lat↗
arXiv2002

Running coupling constant and propagators in SU(2) Landau gauge

We present a numerical study of the running coupling constant and of the gluon and ghost propagators in minimal Landau gauge. Simulations are done in pure SU(2) lattice gauge theory for several values of beta and lattice sizes. We use two different lattice setups.

hep-lat↗
arXiv2002

Fermion-induced quantum action of vortex systems

The quantum action generated by fermions which are minimally coupled to abelian vortex background fields is studied in D=2+1 and D=3+1 Euclidean dimensions. We present a detailed analysis of single- and binary-vortex configurations using the recently developed method of worldline numerics. The dependence of the fermion-induced quantum action on the fermion mass and the magnetic fluxes carried by the vortices is studied, and the binary-vortex interaction is computed. Additionally, we discuss the chiral condensate generated from a dilute gas of vortices in the intermediate fermion mass range for the case D=3+1. As a byproduct, our findings provide insight into the validity limits of the derivative expansion, which is the standard analytical approach to inhomogeneous backgrounds.

hep-th↗
arXiv2002

Vortex induced confinement and the Kugo-Ojima confinement criterion

The SU(2) Yang-Mills gluon and ghost Green-functions are studied in Landau gauge by means of lattice gauge simulations. A focal point is their low energy behavior since in particular the Kugo-Ojima confinement criterion relates a diverging ghost form factor at vanishing momentum transfer to the confining capabilities of the theory. This divergence is verified by numerical simulations. Removing the confining vortices from the lattice ensembles converts SU(2) Yang-Mills theory in a non-confining theory. It is shown that in this modified theory the divergence of the ghost propagator disappears.

hep-lat↗
arXiv2001

Loops and loop clouds - a numerical approach to the worldline formalism in QED -

A numerical technique for calculating effective actions of electromagnetic backgrounds is proposed, which is based on the string-inspired worldline formalism. As examples, we consider scalar electrodynamics in three and four dimensions to one-loop order. Beyond the constant-magnetic-field case, we analyze a step-function-like magnetic field exhibiting a nonlocal and nonperturbative phenomenon: ``magnetic-field diffusion''. Finally, generalizations to fermionic loops and systems at finite temperature are discussed.

hep-ph↗
arXiv2001

Confinement versus color superconductivity: a lattice investigation

High density YM-theory is addressed by means of an effective theory where a Higgs type field corresponds to the diquark order parameter. The effective Higgs theory mimics the Cooper instability at the Fermi surface. After Landau gauge fixing, the theory possesses a global color degree of freedom. Color superconductivity corresponds to a spontaneous breakdown of the residual global color symmetry. Numerical simulations illustrate this mechanism of spontaneously broken global color for the case of the standard electro-weak phase transition and for the case of the transition between the confinement and the Higgs phase, respectively. The latter transition is relevant for the study of diquark condensation.

hep-lat↗
arXiv2001

Quantum diffusion of magnetic fields in a numerical worldline approach

We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar electrodynamics in three dimensions to one-loop order. Beyond the constant-magnetic-field case, serving as a benchmark test, we analyze the effective action of a step-function-like magnetic field -- a configuration that is inaccessible to derivative expansions. We observe magnetic-field diffusion, i.e., nonvanishing magnetic action density at space points near the magnetic step where the classical field vanishes.

hep-ph↗
arXiv2000

Vortex dominance of the 0+ and 2+ glueball mass in SU(2) lattice gauge theory

The c-vortex ensembles are constructed by means of the recently proposed cooling method which gradually removes the SU(2)/Z_2 coset fields from the SU(2) lattice configurations and which thus reveals the Z_2 vortex vacuum texture. Using Teper's blocking method, the screening masses of the 0+ and the 2+ glueball is calculated from these vortex ensembles and compared with the masses obtained from full configurations. The masses of either case agree within the achieved numerical accuracy of 10%. As a byproduct, we find that the overlaps of the Teper operators with the glueball wavefunctions are significantly larger in the case of the c-vortex ensembles.

hep-lat↗
arXiv2000

The gluon condensate from gauge invariant vortex vacuum texture

In SU(2) lattice gauge theory, a new self-restricted cooling procedure is developed to uncover the gauge invariant vortex vacuum texture. The emerging vortex vacuum structure amounts to the full string tension and gives rise to a mass dimension four condensate which is of pure vortex origin.

hep-lat↗
arXiv2000

The Stefan-Boltzmann law: SU(2) versus SO(3) lattice gauge theory

We investigate the high temperature limit of SU(2) and SO(3) lattice gauge theory, respectively. In particular, we study the Stefan-Boltzmann constant in both cases. As is well known, the Stefan-Boltzmann constant extracted from SU(2) lattice gauge theory by incorporating finite size effects is smaller than the continuum value which assumes three gluon degrees of freedom. On the other hand, the extrapolation of our SO(3) lattice data comes much closer to the continuum value. This rises the question whether SU(2) and SO(3) lattice gauge theories represent different quantum theories in the continuum limit.

hep-lat↗
arXiv1999

The non-Abelian dual Meissner effect as color-alignment in SU(2) lattice gauge theory

A new gauge (m-gauge) condition is proposed by means of a generalization of the Maximal Abelian gauge (MAG). The new gauge admits a space time dependent embedding of the residual U(1) into the SU(2) gauge group. This embedding is characterized by a color vector $\vec{m}(x)$. It turns out that this vector only depends of gauge invariant parts of the link configurations. Our numerical results show color ferromagnetic correlations of the $\vec{m}(x)$ field in space-time. The correlation length scales towards the continuum limit. For comparison with the MAG, we introduce a class of gauges which smoothly interpolates between the MAG and the m-gauge. For a wide range of the gauge parameter, the vacuum decomposes into regions of aligned vectors $\vec{m}$. The ''neutral particle problem'' of MAG is addressed in the context of the new gauge class.

hep-lat↗
arXiv1999

Lattice Yang-Mills theory at finite densities of heavy quarks

SU(N_c) Yang-Mills theory is investigated at finite densities of N_f heavy quark flavors. The calculation of the (continuum) quark determinant in the large-mass limit is performed by analytic methods and results in an effective gluonic action. This action is then subject to a lattice representation of the gluon fields and computer simulations. The approach maintains the same number of quark degrees of freedom as in the continuum formulation and a physical heavy quark limit (to be contrasted with the quenched approximation N_f -> 0). The proper scaling towards the continuum limit is manifest. We study the partition function for given values of the chemical potential as well as the partition function which is projected onto a definite baryon number. First numerical results for an SU(2) gauge theory are presented. We briefly discuss the breaking of the color-electric string at finite densities and shed light onto the origin of the overlap problem inherent in the Glasgow approach.

hep-lat↗
arXiv1999

Quark Condensation, Induced Symmetry Breaking and Color Superconductivity at High Density

The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking (ISB). For reasonable strengths for four-Fermi interactions implied by one-gluon exchange quark interactions as well as instanton-mediated interactions, we find that the ISB phase sets in at a moderate density while the quark condensate vanishes, followed by color superconductivity associated with scalar diquark condensation appearing only at an asymptotic density. Lack of confinement in the model makes the result of this analysis only qualitative but the hierarchy of the transitions we find seems to be quite robust.

hep-ph↗
arXiv1999

Vortex percolation and confinement

The vortex state which arises from a projection of SU(2) to $Z_2$ gauge theory is studied at finite temperatures with a special emphasis on the deconfinement phase transition.

hep-lat↗