arXiv subjects

Roman Höllwieser

Publications and source records attributed to Roman Höllwieser.

54 records · Page 3Linked to original sources

arXiv2016

A model of random center vortex lines in continuous 2+1-dimensional space-time

A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. We study both vortex percolation and the potential V (R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.

hep-lat↗

arXiv2016

Two Photon Exchange in Impact Parameter Space in the Relativistic Eikonal Approximation for Elastic e - N Scattering

Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2γ$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimuthally symmetric, the interference term between them is azimuthally asymmetric, which is an indication of an azimuthal single spin asymmetry for proton and neutron which can be attributed to the fact that the nucleon charge density is transversely (azimuthally) distorted in the transverse plane for transversely polarized nucleons. In addition, the calculations of the interference term for proton and neutron show agreement in sign and magnitude of the existence data and calculations for transverse target single spin asymmetry.

hep-ph↗

arXiv2016

Relative weights approach to SU(3) gauge theories with dynamical fermions at finite density

We derive effective Polyakov line actions for SU(3) gauge theories with staggered dynamical fermions, for a small sample of lattice couplings, lattice actions, and lattice extensions in the time direction. The derivation is via the method of relative weights, and the theories are solved at finite chemical potential by mean field theory. We find in some instances that the long-range couplings in the effective action are very important to the phase structure, and that these couplings are responsible for long-lived metastable states in the effective theory. Only one of these states corresponds to the underlying lattice gauge theory.

hep-lat↗

arXiv2016

Confining Bond Rearrangement in the Random Center Vortex Model

We present static meson-meson and baryon--anti-baryon potentials in Z(2) and Z(3) random center vortex models for the infrared sector of Yang-Mills theory, i.e., hypercubic lattice models of random vortex world-surfaces. In particular, we calculate Polyakov loop correlators of two static mesons resp. (anti-)baryons in a center vortex background and observe that their expectation values follow the minimal area law and show bond rearrangement behavior. The static meson-meson and baryon--anti-baryon potentials are compared with theoretical predictions and lattice QCD simulations.

hep-lat↗

arXiv2015

Polyakov line actions from $SU(3)$ lattice gauge theory with dynamical fermions: first results via relative weights

We apply the relative weights method to extract an effective Polyakov line action, at finite chemical potential, from an underlying $SU(3)$ lattice gauge theory with dynamical fermions. The center-symmetry breaking terms in the effective theory are fit to a form suggested by the hopping-parameter expansion, and the effective action is solved at finite chemical potential by a mean field approach. We present preliminary results for one-link staggered fermions with mass $ma=1.0$ and Wilson gauge action at $β=5.4$ on $L^3\times4$ lattices with $L=16$.

hep-lat↗

arXiv2015

Colorful plane vortices and Chiral Symmetry Breaking in $SU(2)$ Lattice Gauge Theory

We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the winding number between the two vacua, leading to a topological charge $Q=-1$ in the continuum. After growing temporal extent of these vortices, the lattice topological charge approaches $-1$ and the index theorem is fulfilled. We analyze the low lying modes of the overlap Dirac operator in the background of these colorful plane vortices and compare them with those of spherical vortices. They show characteristic properties for spontaneous chiral symmetry breaking.

hep-lat↗

arXiv2015

Approaching $SU(2)$ gauge dynamics with smeared $Z(2)$ vortices

We present a method to smear (center projected) $Z(2)$ vortices in lattice gauge configurations such as to embed vortex physics into a full $SU(2)$ gauge configuration framework. In particular, we address the problem that using $Z(2)$ configurations in conjunction with overlap (or chirally improved) fermions is problematic due to their lack of smoothness. Our method allows us to regain this smoothness and simultaneously maintain the center vortex structure. We verify our method with various gluonic and fermionic observables.

hep-lat↗

arXiv2015

Center Vortices, Area Law and the Catenary Solution

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.

hep-lat↗

arXiv2015

Smearing Center Vortices

We smear Z(2) center vortices in lattice gauge configurations such as to recover thick vortices with full SU(2) Yang-Mills information. In particular, we address the problem that using Z(2) configurations in conjunction with overlap (or chirally improved) fermions is problematic due to their lack of smoothness. Our method allows us to regain this smoothness and simultaneously maintain the center vortex structure. We verify our method with various gluonic and fermionic observables and find good agreement between smeared vortex configurations and full SU(2).

hep-lat↗

arXiv2015

Center Vortex vs. Abelian models of the QCD vacuum

We present evidence that the center vortex model of confinement is more consistent with lattice results than other currently available models. In particular we show that Abelian field distributions predicted by monopole plasma, caloron gas or dual superconductor models cannot reproduce the area-law falloff of double winding Wilson loops in full $SU(2)$ and center vortex only gauge fields.

hep-lat↗

arXiv2014

Double-winding Wilson loops and monopole confinement mechanisms

We consider "double-winding" Wilson loops in SU(2) gauge theory. These are contours which wind once around a loop $C_1$ and once around a loop $C_2$, where the two co-planar loops share one point in common, and where $C_1$ lies entirely in (or is displaced slightly from) the minimal area of $C_2$. We discuss the expectation value of such double-winding loops in abelian confinement pictures, where the spatial distribution of confining abelian fields is controlled by either a monopole Coulomb gas, a caloron ensemble, or a dual abelian Higgs model, and argue that in such models an exponential falloff in the sum of areas $A_1+A_2$ is expected. In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas $A_2-A_1$. We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law. The conclusion is that even if confining gluonic field fluctuations are, in some gauge, mainly abelian in character, the spatial distribution of those abelian fields cannot be the distribution predicted by the simple monopole gas, caloron ensemble, or dual abelian Higgs actions, which have been used in the past to explain the area law falloff of Wilson loops.

hep-lat↗

arXiv2014

Random center vortex lines in continuous 3D space-time

We present a model of center vortices, represented by closed random lines in continuous 2+1- dimensional space- time. These random lines are modeled as being piece-wise linear and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a cuboid with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configuration, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. Using the model, we study both vortex percolation and the potential V (R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We have found three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature. The model reproduces the qualitative features of confinement physics seen in SU(2) Yang-Mills theory.

hep-lat↗

arXiv2014

Chiral Symmetry Breaking from Center Vortices

We analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from classical center vortices in SU(2) lattice gauge theory. We show that colorful spherical vortex and instanton configurations have very similar Dirac eigenmodes and also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the influence of the magnetic vortex fluxes on quarks and how center vortices may break chiral symmetry.

hep-lat↗

arXiv2013

Center Vortices and Chiral Symmetry Breaking in SU(2) Lattice Gauge Theory

We investigate the chiral properties of near-zero modes for thick classical center vortices in SU (2) lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.

hep-lat↗

arXiv2013

Colorful SU(2) center vortices in the continuum and on the lattice

The spherical vortex as introduced in [Phys. Rev. D77, 014515 (2008)] is generalized. A continuum form of the spherical vortex is derived and investigated in detail. The discrepancy between the gluonic lattice topological charge and the index of the lattice Dirac operator described in previous papers is identified as a discretization effect. The importance of the investigations for Monte Carlo configurations is discussed.

hep-lat↗

arXiv2011

Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory

Intersections of thick, plane SU(2) center vortices are characterized by the topological charge |Q|=1/2. We compare such intersections with the distribution of zeromodes of the Dirac operator in the fundamental and adjoint representation using both the overlap and asqtad staggered fermion formulations in SU(2) lattice gauge theory. We analyze configurations with four intersections and find that the probability density distribution of fundamental zeromodes in the intersection plane differs significantly from the one obtained analytically in [Phys.\ Rev.\ D 66, 85004 (2002)]. The Dirac eigenmodes are clearly sensitive to the traces of the Polyakov (Wilson) lines and do not exactly locate topological charge contributions. Although, the adjoint Dirac operator is able to produce zeromodes for configurations with topological charge |Q|=1/2, they do not locate single vortex intersections, as we prove by forming arbitrary linear combinations of these zeromodes - their scalar density peaks at least at two intersection points. With pairs of thin and thick vortices we realize a situation similar to configurations with topological charge |Q|=1/2. For such configurations the zeromodes do not localize in the regions of fractional topological charge contribution but spread over the whole lattice, avoiding regions of negative traces of Polyakov lines.

hep-lat↗

arXiv2010

Lattice Index Theorem and Fractional Topological Charge

We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In particular we address the puzzle raised in a previous work of our group [Phys.\ Rev.\ D 77, 14515 (2008)], where we found a violation of the lattice index theorem with the overlap Dirac operator in the fundamental representation even for "admissible" gauge fields. Here we confirm the discrepancy between the topological charge and the index of the Dirac operator also for asqtad staggered fermions and the adjoint representation. Numerically, the discrepancy equals the sum of the winding numbers of the spheres when they are regarded as maps $\mathbbm R^3 \cup \{\infty\} \to SU(2)$. Furthermore we find some evidence for fractional topological charge during cooling the spherical center vortex on a $40^3 \times 2$ lattice. The object with topological charge $Q=1/2$ we identify as a Dirac monopole with a gauge field fading away at large distances. Therefore even for periodic boundary conditions it does not need an antimonopole.

hep-lat↗

arXiv2008

Center Vortices and the Dirac Spectrum

We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. In particular we address a puzzle raised some years ago by Gattnar et al. [Nucl. Phys. B 716, 105 (2005)], who noted that the low-lying Dirac eigenmodes required for chiral symmetry breaking do not appear to be present in center-projected configurations. We show that the low-lying modes are in fact present in the staggered (asqtad) formulation, but not in the overlap and ``chirally improved'' formulations, and suggest a reason for this difference. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], showing that there is a correlation between center vortex locations, and the scalar density of low-lying Dirac eigenmodes derived from unprojected configurations. This correlation is strongest at points which are associated, in the vortex picture, with non-vanishing topological charge density, such as vortex intersection and ``writhing'' points. We present supporting evidence that the lowest Dirac eigenmodes, in both asqtad and overlap formulations, have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality.

hep-lat↗