Impact of Dynamical Fermions on QCD Vacuum Structure

We examine how dynamical fermions affect both the UV and infrared structure of the QCD vacuum. We consider large $28^3 \times 96$ lattices from the MILC collaboration, using a gluonic definition of the topological charge density, founded on a new over-improved stout-link smearing algorithm. The algorithm reproduces established results from the overlap formalism and is designed to preserve nontrivial topological objects including instantons. At short distances we focus on the topological charge correlator, , where negative values at small $x$ reveal a sign-alternating layered structure to the topological-charge density of the QCD vacuum. We find that the magnitudes of the negative dip in the correlator and the positive $$ contact term are both increased with the introduction of dynamical fermion degrees of freedom. This is in accord with expectations based on charge renormalization and the vanishing of the topological susceptibility in the chiral limit. At large distances we examine the extent to which instanton-like objects are found on the lattice, and how their distributions vary between quenched and dynamical gauge fields. We show that dynamical gauge fields contain more instanton-like objects with an average size greater than in the quenched vacuum. Finally, we directly visualize the topological charge density in order to investigate the effects of dynamical sea-quark degrees of freedom on topology.Comment: 9 pages, 8 figure

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Improved superposition schemes for approximate multi-caloron configurations

Two improved superposition schemes for the construction of approximate multi-caloron-anticaloron configurations, using exact single (anti)caloron gauge fields as underlying building blocks, are introduced in this paper. The first improvement deals with possible monopole-Dirac string interactions between different calorons with non-trivial holonomy. The second one, based on the ADHM formalism, improves the (anti-)selfduality in the case of small caloron separations. It conforms with Shuryak's well-known ratio-ansatz when applied to instantons. Both superposition techniques provide a higher degree of (anti-)selfduality than the widely used sum-ansatz, which simply adds the (anti)caloron vector potentials in an appropriate gauge. Furthermore, the improved configurations (when discretized onto a lattice) are characterized by a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly shortened, changes in the introduction, new results added on the comparison with exact solution

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

An SU(2) KvBLL caloron gas model and confinement

A semi-classical model is developed to describe pure SU(2) Yang-Mills gluodynamics at finite temperature as a dilute, non-interacting gas of Kraan-van Baal-Lee-Lu calorons including the case of non-trivial holonomy. Temperature dependent parameters of the model (asymptotic caloron holonomy, caloron density and caloron size distribution) are discussed from the point of view of lattice observations and of in-medium modifications of the one-loop caloron amplitude. Space-like string tensions running into plateaux at distances R \approx 0.8 - 1.3 fm are obtained and compared to lattice results in order to find more precisely the average caloron size. Then, the quark-antiquark free energy as predicted by the model is considered. In the confined phase a linear rise with the separation can be observed up to R \approx 4 fm, whereas it runs into plateaux above T_c. Screening effects in the adjoint potentials are observed together with an approximate Casimir scaling of the caloron contribution to the fundamental and adjoint forces. In Abelian projection, space-like percolation of monopoles is found in the confined phase only. Thus, taking the non-trivial holonomy into account, confinement properties of pure SU(2) Yang-Mills gluodynamics can be described by a semi-classical approach up to distances one order of magnitude larger than the caloron size.Comment: 26 pages, 14 figures, textheight change

Dressed Polyakov loop and flavor dependent phase transitions

The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of Nf = 2+1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate and dressed Polyakov loop differ in a narrow transition range in the lower baryon density region, and the two transitions coincide in the higher baryon density region.Comment: 9 pages, 9 figures; Version accepted in Phys. Rev.

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ

Numerical properties of staggered quarks with a taste-dependent mass term

The numerical properties of staggered Dirac operators with a taste-dependent mass term proposed by Adams [1,2] and by Hoelbling [3] are compared with those of ordinary staggered and Wilson Dirac operators. In the free limit and on (quenched) interacting configurations, we consider their topological properties, their spectrum, and the resulting pion mass. Although we also consider the spectral structure, topological properties, locality, and computational cost of an overlap operator with a staggered kernel, we call attention to the possibility of using the Adams and Hoelbling operators without the overlap construction. In particular, the Hoelbling operator could be used to simulate two degenerate flavors without additive mass renormalization, and thus without fine-tuning in the chiral limit.Comment: 14 pages, 9 figures. V2: published version; important note added regarding Hoelbling fermions, otherwise minor change

Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge

Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.