A detailed comparison is made between the topological structure of quenched QCD as revealed by th... more A detailed comparison is made between the topological structure of quenched QCD as revealed by the recently proposed over-improved stout-link smearing in conjunction with an improved gluonic definition of the topological density on one hand and a similar analysis made possible by the overlapfermionic topological charge density both with and without variable ultraviolet cutoff λcut. The matching is twofold, provided by fitting the density-density two-point functions on one hand and by a point-by-point fitting of the topological densities according to the two methods. We point out the similar cluster structure of the topological density for moderate smearing and 200 MeV < λcut < 600 MeV, respectively. We demonstrate the relation of the gluonic topological density for extensive smearing to the location of the overlap zero modes and the lowest overlap non-zero mode as found for the unsmeared configurations.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We estimate the running coupling constant of the strong interactions within the nonperturbative f... more We estimate the running coupling constant of the strong interactions within the nonperturbative framework of lattice QCD in Landau gauge. Our calculation is based on the ghost-gluon vertex which in the particular case of Landau gauge allows for a definition of α s in a MOM scheme solely in terms of the gluon and ghost dressing functions. As a first step we investigate the zero and two-flavour case and report here on preliminary results.
Proceedings of XXIVth International Symposium on Lattice Field Theory — PoS(LAT2006), 2006
We summarize the current status of our numerical results for the gluon and ghost propagators and ... more We summarize the current status of our numerical results for the gluon and ghost propagators and for the Kugo-Ojima confinement parameter in quenched SU(3) lattice Landau gauge theory. The data for the propagators are compared to our results obtained in the case of full QCD, simulated using two flavors of dynamical clover-improved Wilson fermions. We demonstrate that the infrared behavior of the ghost propagator is consistent with the Kugo-Ojima confinement criterion. Explicit violation of reflection positivity by the gluon propagator is shown. Additionally, we present results of a running coupling constant both at low and at large momenta.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size... more The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size of 32 3 × 200. We use the standard Wilson action at β = 6.0 and compare our results with previous computations using large asymmetric and symmetric lattices. In particular, we focus on the impact of the lattice geometry and momentum cuts to achieve compatibility between data from symmetric and asymmetric lattices for a large range of momenta.
In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature latt... more In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action. We present a first feasibility study at maximal twist and, for the quenched case, we demonstrate automatic O(a)-improvement to work.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As... more We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As a prerequisite for a future analysis of the finite-temperature transition making use of automatic O(a) improvement, we investigate the phase structure in the space spanned by the hopping parameter κ, the coupling β , and the twisted mass parameter µ. We present results for N f = 2 degenerate quarks on a 16 3 × 8 lattice, for which we investigate the possibility of an Aoki phase existing at strong coupling and vanishing µ, as well as of a thermal phase transition at moderate gauge couplings and non-vanishing µ.
We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for... more We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for a set of pion masses, 300 MeV <mπ <500 MeV, and lattice spacings a <0.09 fm. We determine the pseudo-critical temperatures and discuss their extrapolation to the chiral limit using scaling forms for different universality classes, as well as the scaling form for the magnetic equation of state. For all pion masses considered we find resonable consistency with O(4) scaling plus leading corrections. However, a true distinction between the O(4) scenario and a first order scenario in the chiral limit requires lighter pions than are currently in use in simulations of Wilson fermions.
We discuss Monte Carlo results relevant to the deconfinement order parameter and its fluctuation ... more We discuss Monte Carlo results relevant to the deconfinement order parameter and its fluctuation from the viewpoint of the dilute instanton gas approximation. We find a threshold effect in the Wilson string distribution due to instanton effects. On the basis of these data we determine a relation between the saturation temperature of the instanton gas and the confinement temperature. We also present other results of the numerical calculation.
We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian... more We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on spacelike hyperplanes) to the theory on the Light Front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice.
Starting from the QCD Hamiltonian in near-light cone coordinates, we study the dynamics of the gl... more Starting from the QCD Hamiltonian in near-light cone coordinates, we study the dynamics of the gluonic zero modes. Euclidean 2+1 dimensional lattice simulations show that the gap at strong coupling vanishes at intermediate coupling. This result opens the possibility to synchronize the continuum limit with the approach to the light cone.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the... more We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r 0 Λ (0) MS = 0.62(1) and r 0 Λ (2) MS = 0.60(3)(2), with the second error due to an extrapolation uncertainty.
The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU (3) gauge theo... more The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU (3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects at temperatures close to the deconfinement phase transition at T = Tc and within the restricted range of momenta. Since the longitudinal component DL(q) turns out to be most sensitive with respect to the phase transition we propose some combinations of DL(q) signalling the transition much like "order parameters".
We study the properties of configurations from which P-vortices on one hand or Abelian monopoles ... more We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q index = 0. The remaining (ultraviolet) monopoles without vortices and-to a less extent-the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.
Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool fo... more Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.
We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the... more We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r 0 Λ (0) MS = 0.62(1) and r 0 Λ
The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU(3) gauge theor... more The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU(3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects
We study the properties of configurations from which P-vortices on one hand or Abelian monopoles ... more We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q index = 0. The remaining (ultraviolet) monopoles without vortices and -to a less extent -the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.
Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool fo... more Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zerotemperature quenched SU(3) configurations generated by means of the Lüscher-Weisz action, we define the topological charge density with and without UV filtering and study its properties by looking at the density profile and the two-point correlation function. We observe that the density possesses global sign coherent structures, which get increasingly tangled as more and more modes are included. This change of the structure is also detected by the increasing negative tail of the two-point function. We also study the inverse participation ratio of the eigenmodes and discuss their dimensionality.
Overlap fermions are particularly well suited to study the finite temperature dynamics of the chi... more Overlap fermions are particularly well suited to study the finite temperature dynamics of the chiral symmetry restoration transition of QCD, which might be just an analytic crossover. Using gauge field configurations on a 24^3x10 lattice with N_f=2 flavours of dynamical Wilson-clover quarks generated by the DIK collaboration, we compute the lowest 50 eigenmodes of the overlap Dirac operator and try to locate the transition by fermionic means. We analyse the spectral density, local chirality and localisation properties of the low-lying modes and illustrate the changing topological and (anti-) selfdual structure of the underlying gauge fields across the transition.
A detailed comparison is made between the topological structure of quenched QCD as revealed by th... more A detailed comparison is made between the topological structure of quenched QCD as revealed by the recently proposed over-improved stout-link smearing in conjunction with an improved gluonic definition of the topological density on one hand and a similar analysis made possible by the overlapfermionic topological charge density both with and without variable ultraviolet cutoff λcut. The matching is twofold, provided by fitting the density-density two-point functions on one hand and by a point-by-point fitting of the topological densities according to the two methods. We point out the similar cluster structure of the topological density for moderate smearing and 200 MeV < λcut < 600 MeV, respectively. We demonstrate the relation of the gluonic topological density for extensive smearing to the location of the overlap zero modes and the lowest overlap non-zero mode as found for the unsmeared configurations.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We estimate the running coupling constant of the strong interactions within the nonperturbative f... more We estimate the running coupling constant of the strong interactions within the nonperturbative framework of lattice QCD in Landau gauge. Our calculation is based on the ghost-gluon vertex which in the particular case of Landau gauge allows for a definition of α s in a MOM scheme solely in terms of the gluon and ghost dressing functions. As a first step we investigate the zero and two-flavour case and report here on preliminary results.
Proceedings of XXIVth International Symposium on Lattice Field Theory — PoS(LAT2006), 2006
We summarize the current status of our numerical results for the gluon and ghost propagators and ... more We summarize the current status of our numerical results for the gluon and ghost propagators and for the Kugo-Ojima confinement parameter in quenched SU(3) lattice Landau gauge theory. The data for the propagators are compared to our results obtained in the case of full QCD, simulated using two flavors of dynamical clover-improved Wilson fermions. We demonstrate that the infrared behavior of the ghost propagator is consistent with the Kugo-Ojima confinement criterion. Explicit violation of reflection positivity by the gluon propagator is shown. Additionally, we present results of a running coupling constant both at low and at large momenta.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size... more The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size of 32 3 × 200. We use the standard Wilson action at β = 6.0 and compare our results with previous computations using large asymmetric and symmetric lattices. In particular, we focus on the impact of the lattice geometry and momentum cuts to achieve compatibility between data from symmetric and asymmetric lattices for a large range of momenta.
In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature latt... more In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action. We present a first feasibility study at maximal twist and, for the quenched case, we demonstrate automatic O(a)-improvement to work.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As... more We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As a prerequisite for a future analysis of the finite-temperature transition making use of automatic O(a) improvement, we investigate the phase structure in the space spanned by the hopping parameter κ, the coupling β , and the twisted mass parameter µ. We present results for N f = 2 degenerate quarks on a 16 3 × 8 lattice, for which we investigate the possibility of an Aoki phase existing at strong coupling and vanishing µ, as well as of a thermal phase transition at moderate gauge couplings and non-vanishing µ.
We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for... more We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for a set of pion masses, 300 MeV <mπ <500 MeV, and lattice spacings a <0.09 fm. We determine the pseudo-critical temperatures and discuss their extrapolation to the chiral limit using scaling forms for different universality classes, as well as the scaling form for the magnetic equation of state. For all pion masses considered we find resonable consistency with O(4) scaling plus leading corrections. However, a true distinction between the O(4) scenario and a first order scenario in the chiral limit requires lighter pions than are currently in use in simulations of Wilson fermions.
We discuss Monte Carlo results relevant to the deconfinement order parameter and its fluctuation ... more We discuss Monte Carlo results relevant to the deconfinement order parameter and its fluctuation from the viewpoint of the dilute instanton gas approximation. We find a threshold effect in the Wilson string distribution due to instanton effects. On the basis of these data we determine a relation between the saturation temperature of the instanton gas and the confinement temperature. We also present other results of the numerical calculation.
We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian... more We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on spacelike hyperplanes) to the theory on the Light Front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice.
Starting from the QCD Hamiltonian in near-light cone coordinates, we study the dynamics of the gl... more Starting from the QCD Hamiltonian in near-light cone coordinates, we study the dynamics of the gluonic zero modes. Euclidean 2+1 dimensional lattice simulations show that the gap at strong coupling vanishes at intermediate coupling. This result opens the possibility to synchronize the continuum limit with the approach to the light cone.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the... more We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r 0 Λ (0) MS = 0.62(1) and r 0 Λ (2) MS = 0.60(3)(2), with the second error due to an extrapolation uncertainty.
The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU (3) gauge theo... more The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU (3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects at temperatures close to the deconfinement phase transition at T = Tc and within the restricted range of momenta. Since the longitudinal component DL(q) turns out to be most sensitive with respect to the phase transition we propose some combinations of DL(q) signalling the transition much like "order parameters".
We study the properties of configurations from which P-vortices on one hand or Abelian monopoles ... more We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q index = 0. The remaining (ultraviolet) monopoles without vortices and-to a less extent-the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.
Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool fo... more Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.
We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the... more We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r 0 Λ (0) MS = 0.62(1) and r 0 Λ
The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU(3) gauge theor... more The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU(3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects
We study the properties of configurations from which P-vortices on one hand or Abelian monopoles ... more We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q index = 0. The remaining (ultraviolet) monopoles without vortices and -to a less extent -the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.
Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool fo... more Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zerotemperature quenched SU(3) configurations generated by means of the Lüscher-Weisz action, we define the topological charge density with and without UV filtering and study its properties by looking at the density profile and the two-point correlation function. We observe that the density possesses global sign coherent structures, which get increasingly tangled as more and more modes are included. This change of the structure is also detected by the increasing negative tail of the two-point function. We also study the inverse participation ratio of the eigenmodes and discuss their dimensionality.
Overlap fermions are particularly well suited to study the finite temperature dynamics of the chi... more Overlap fermions are particularly well suited to study the finite temperature dynamics of the chiral symmetry restoration transition of QCD, which might be just an analytic crossover. Using gauge field configurations on a 24^3x10 lattice with N_f=2 flavours of dynamical Wilson-clover quarks generated by the DIK collaboration, we compute the lowest 50 eigenmodes of the overlap Dirac operator and try to locate the transition by fermionic means. We analyse the spectral density, local chirality and localisation properties of the low-lying modes and illustrate the changing topological and (anti-) selfdual structure of the underlying gauge fields across the transition.
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Papers by E. Ilgenfritz