In Quantum Chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of ρ and a1 approach each other) while confining properties persist.PACS numbers: 11.15.Ha, 12.38.Gc I. MOTIVATION AND INTRODUCTIONDynamical chiral symmetry breaking in QCD is associated with the low lying spectral modes of the Dirac operator D [1]. They affect the path integral weight of the gauge configurations through the determinant of D.As indicated by the Atiyah-Singer index theorem [2], the exact zero modes are related to topological excitations, the instantons. For Dirac operators violating chiral symmetry these are real eigenmodes. The nearby non-real modes are also thought to be related to composed structure of, e.g., overlapping instantons [3]. 1 In a series of papers [4][5][6] it was emphasized that low modes saturate the pseudoscalar and axial vector correlators at large distances and do not affect the part where high-lying states appear. In [6,7] low mode saturation and also effects of low mode removal for mesons were studied for quenched configurations with the overlap Dirac operator [8,9].Subsequently low modes were utilized to improve the convergence of the determination of hadron propagators [6,7,10,11] (see also the recent study [12,13] comparing the efficiency when using the low modes of the Dirac operator or the hermitian Dirac operator, where strong dependence on the parity of the hadron states was presented).Associating the low mode sector with the nonperturbative chiral symmetry breaking and the condensate [1], a complementary question is how important it is for confinement and mass generation of hadrons. Here we study what happens, if one removes up to 512 low lying modes from the valence quark sector. We compute propagators of the pion and other mesons and determine the effect of this removal on the mass spectrum. This way we want to shed light on the role of the condensate related to * christian.lang@uni-graz.at † mario.schroeck@uni-graz.at 1 Even when studying the low lying modes in quenched gauge ensembles one observes non-vanishing density and also the GellMann-Oakes-Renner relation works down to small values of the valence quark mass until quenched chiral logs destroy the leading chiral symmetry breaking behavior. the spectral part of the Dirac operator in confinement and chiral symmetry breaking. Our analysis is done for configurations generated for two light, mass degenerate dynamical quark flavors. The removal of the low lying modes is effective only in the valence quarks sector. However, as will be seen, this already has significant impact on the meson mass spectrum.In [14,15] it has been conjectured that chiral symmetr...

We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U (1)A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the ∆ − N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.

We calculate the lattice quark propagator in Coulomb gauge from both dynamical and quenched configurations. We show that in the continuum limit both the static and the full quark propagators are multiplicatively renormalizable. From the propagator we extract the quark renormalization function ZðjpjÞ and the running mass MðjpjÞ and extrapolate the latter to the chiral limit. We find that MðjpjÞ practically coincides with the corresponding Landau gauge function for small momenta. The computation of MðjpjÞ can, however, be made more efficient in Coulomb gauge; this can lead to a better determination of the chiral mass and the quark anomalous dimension. Moreover from the structure of the full propagator we can read an expression for the dispersion relation of quarks, compatible with an IR divergent effective energy. If confirmed on larger volumes, this finding would allow one to extend the Gribov-Zwanziger confinement mechanism to the fermionic sector of QCD.

A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single (SP) and double precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed precision scheme that performs the critical parts of the algorithm in full DP while retaining 80-90% of the SP performance. Finally, multi-GPUs are adopted to overcome the memory constraint of single GPUs. A communicator class which hides the MPI data exchange at the boundaries of the lattice domains, via the low bandwidth PCI-Bus, effectively behind calculations in the inner part of the domain is presented. Linear scaling using 16 NVIDIA Tesla C2070 devices and a maximum performance of 3.5 Teraflops on lattices of size down to 64 3 × 256 is demonstrated.

The chirally improved (CI) quark propagator in Landau gauge is calculated in two flavor lattice Quantum Chromodynamics. Its wave-function renormalization function Z(p 2 ) and mass function M (p 2 ) are studied. To minimize lattice artifacts, tree-level improvement of the propagator and treelevel correction of the lattice dressing functions is applied. Subsequently the CI quark propagator under Dirac operator low-mode removal is investigated. The dynamically generated mass in the infrared domain of the mass function is found to dissolve continuously as a function of the reduction level and strong suppression of Z(p 2 ) for small momenta is observed.