Search

We study lattice QCD with $N_f=2$ Wilson fermions at nonzero imaginary chemical potential and nonzero temperature. We relate the Roberge - Weiss phase transition to the properties of dyons which are constituents of the KvBLL calorons. We present numerical evidence that the characteristic features of the spectral gap of the overlap Dirac operator as function of an angle modifying the boundary condition are determined by the $Z_3$ sector of the respective imaginary chemical potential. We then demonstrate that dyon excitations in thermal configurations could be responsible (in line with perturbative excitations) for these phenomena., Comment: 10 pages, 5 figures, Contribution to XIIth Quark Confinement and the Hadron Spectrum

We study the topological structure of QCD by cluster analysis. The fermionic topological charge density is constructed from low lying modes of overlap Dirac operator for three types of temporal boundary conditions for fermion field. This gives the possibility to mark all three dyon constitutents of KvBLL caloron in gluonic fields. The gluonic topological charge density is appearing in the process of overimproved gradient flow process stopped at the moment when it maximally matches the fermionic topological charge density. This corresponds to the smearing of gluonic fields up to the scale set by dyon size. The time-like Abelian monopoles and specific KvBLL pattern of Polyakov line correlate with topological clusters., 12 pages, 6 figures. Corrected HUB preprint number, restored missing temperature scale, changed subsections of section III. arXiv admin note: text overlap with arXiv:1410.4632

This article in honor of Yurii Antonovich Simonov’s 70th birthday reviews some recent work related to the semiclassical approach to QCD at finite temperature based on classical solutions with nontrivial holonomy. By cooling Monte Carlo generated lattice SU(2) gauge fields, we investigate approximate solutions of the classical field equations as a possible starting point for rethinking the semiclassical approximation of the path integral. We show that old findings of cooling have to be reinterpreted in terms of Kraan-van Baal solutions with generically nontrivial holonomy instead of Harrington-Shepard caloron solutions with trivial holonomy. The latter represent only a subclass of possible topological configurations and for T < Tc seem to become suppressed due to quantum fluctuations.

We discuss recent solutions for SU(2) calorons with non-trivial holonomy at higher charge, both through analytic means and using cooling, as well as extensive lattice studies for SU(3)., 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice 2004(topology)

The topological structure of lattice gluodynamics is studied at intermediate resolution scale in the deconfining phase with the help of a cluster analysis. UV filtered topological charge densities are determined from a fixed number of low-lying eigenmodes of the overlap Dirac operator with three types of temporal boundary conditions applied to the valence quark fields. This method usually allows to find all three distinguished (anti)dyon constituents in the gauge field of Kraan-van Baal-Lee-Lu (anti)caloron solutions. The clustering of the three topological charge densities in Monte Carlo generated configurations is then used to mark the positions of anticipated (anti)dyons of the corresponding type. In order to support this interpretation, inside these clusters, we search also for time-like Abelian monopole currents (defined in the maximally Abelian gauge) as well as for local holonomies with at least two approximately degenerated eigenvalues. Our results support the view that light dyon-antidyon pairs - in contrast to the heavy (anti)caloron dyon constituents - contribute dominantly to thermal Yang-Mills fields in the deconfinement phase. This paper is dedicated to the memory of Pierre van Baal and Dmitri Igorevich Diakonov who have influenced our work very much., 15 pages, 10 figures

Topological objects of $SU(3)$ gluodynamics are studied at the infrared scale near the transition temperature with the help of zero and near-zero modes of the overlap Dirac operator. We construct UV filtered topological charge densities corresponding to three versions of the temporal boundary condition applied to this operator, for which the zero mode is known to be located on corresponding three constituent dyons (antidyons) in the reference case of an analytical (anti)caloron solution. The clustering of the three topological charge densities marks the positions of three types of dyons and antidyons which can therefore be considered as present in equilibrium (Monte Carlo) gluonic fields at the given resolution scale. We classify them either as constituents of nondissociated (anti)calorons or as constituents of (anti)dyon pairs or as isolated (anti)dyons. The pattern of the Polyakov loop describing the centers and the interior of these clusters is observed after a limited number of overimproved cooling steps and resembles the description known from analytical caloron solutions., 12 pages, 9 figures; revised version accepted by Phys. Rev. D

Gluodynamics and two-flavor QCD at non-zero temperature are studied with the so-called overimproved cooling technique under which caloron solutions may remain stable. We consider topological configurations either at the first occuring stable plateau of topological charge or at the first (anti)selfdual plateau and find the corresponding topological susceptibility at various temperatures on both sides of the thermal transition or crossover. In pure gluodynamics the topological susceptibility drops sharply at the deconfinement temperature while in full QCD it decreases smoothly at temperatures above the pseudocritical one. The results are close to those calculated by other methods. We interpret our findings in terms of the (in)stability of calorons with non-trivial holonomy and their dyon constituents against overimproved cooling., 10 pages, 9 figures

Using a standard cooling method for SU(3) lattice gauge fields constant Abelian magnetic field configurations are extracted after dyon-antidyon constituents forming metastable Q=0 configurations have annihilated. These so-called Dirac sheets, standard and non-standard ones, corresponding to the two U(1) subgroups of the SU(3) group, have been found to be stable if emerging from the confined phase, close to the deconfinement phase transition, with sufficiently nontrivial Polyakov loop values. On a finite lattice we find a nice agreement of the numerical observations with the analytic predictions concerning the stability of Dirac sheets depending on the value of the Polyakov loop.

We reveal the center vortex content of SU(2) calorons and ensembles of them. While one part of the vortex connects the constituent dyons of a single caloron, another part is predominantly spatial and can be related to the twist that exists in the caloron gauge field. The latter part depends strongly on the caloron holonomy and degenerates to a plane between the dyons when the asymptotic Polyakov loop is traceless. Correspondingly, the spatial vortex in caloron ensembles is percolating in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex (de)confinement mechanism., AIP Conf. Proc. 1343

We reveal the center vortex content of SU(2) calorons and ensembles of them. We use Laplacian center gauge as well as maximal center gauges to show that the vortex in a single caloron consists of two parts. The first one connects the constituent dyons of the caloron (which are monopoles in Laplacian Abelian gauge) and extends in time. The second part is predominantly spatial, encloses one of the dyons and can be related to the twist in the caloron gauge field. This part depends strongly on the caloron holonomy and degenerates to a plane when the holonomy is maximally nontrivial, i.e. when the asymptotic Polyakov loop is traceless. Correspondingly, we find the spatial vortices in caloron ensembles to percolate in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex confinement mechanism.

In the deconfinement phase of quenched SU(2) Yang-Mills theory the spectrum and localization properties of the eigenmodes of the overlap Dirac operator with antiperiodic boundary conditions are strongly dependent on the sign of the average Polyakov loop, $$. For $ > 0$ a gap appears with only few, highly localized topological zero and near-zero modes separated from the rest of the spectrum. Instead of a gap, for $ < 0$ a high spectral density of relatively delocalized near-zero modes is observed. In an ensemble of positive $$, the same difference of the spectrum appears under a change of fermionic boundary conditions. We argue that this effect and other properties of near-zero modes can be explained through the asymmetric properties and the different abundance of dyons and antidyons -- topological objects also known to appear, however in a symmetric form, in the confinement phase at $T < T_c$ as constituents of calorons with maximally nontrivial holonomy., Comment: 12 pages, 7 figures. Clarifying changes in the introduction, no results changed; data added, 1 figure added, last changes to match article in Phys.Rev. D

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 nonzero 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 ${Q}_{\mathrm{index}}=0$. The remaining (ultraviolet) monopoles without vortices and\char22{}to a less extent\char22{}the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble affects the monopoles and vortices only by smoothing, reducing the density only slightly.

In a pilot study, we use the topological charge density defined by the eigenmodes of the overlap Dirac operator (with ultraviolet filtering by mode-truncation) to search for lumps of topological charge in SU(2) pure gauge theory. Augmenting this search with periodic and antiperiodic temporal boundary conditions for the overlap fermions, we demonstrate that the lumps can be classified either as calorons or as separate caloron constituents (dyons). Inside the topological charge clusters the (smeared) Polyakov loop is found to show the typical profile characteristic for calorons and dyons. This investigation, motivated by recent caloron/dyon model studies, is performed at the deconfinement phase transition for SU(2) gluodynamics on 20^3 x 6 lattices described by the tadpole improved L\"uscher-Weisz action. The transition point has been carefully located. As a necessary condition for the caloron/dyon detection capability, we check that the LW action, in contrast to the Wilson action, generates lattice ensembles, for which the overlap Dirac eigenvalue spectrum smoothly behaves under smearing and under the change of the boundary conditions., Comment: 17 pages, 8 figures, minor changes (typos, grants, ..)

In this talk, relying on experience with various lattice filter techniques, we argue that the semiclassical structure of finite temperature gauge fields for T < T_c is dominated by calorons with non-trivial holonomy. By simulating a dilute gas of calorons with identical holonomy, superposed in the algebraic gauge, we are able to reproduce the confining properties below T_c up to distances r = O(4 fm} >> ��(the caloron size). We compute Polyakov loop correlators as well as space-like Wilson loops for the fundamental and adjoint representation. The model parameters, including the holonomy, can be inferred from lattice results as functions of the temperature., Talk by M. M\"uller-Preussker at "Quark Confinement and Hadron Structure VII", Ponta Delgada, Azores, Portugal, September 2 - 7, 2006, 4 pages, 2 figures, to appear in the Proceedings

Institute for Theoretical and Experimental Physics,B. Cheremushkinskaya 25, Moscow 117259, RussiaIn equilibrium, at finite temperature below and above the deconfining phase transition, we havegenerated lattice SU(2) gauge fields and have exposed them to smearing in order to investigate theemerging clusters of topological charge. Analysing in addition the monopole clusters according tothe maximally Abelian gauge, we have been able to characterize part of the topological clusters tocorrespond either to non-static calorons or static dyons in the context of Kraan-van Baal caloronsolutions with non-trivial holonomy. We show that the relative abundance of these calorons anddyons is changing with temperature and offer an interpretation as dissociation of calorons into dyonswith increasing temperature. The profile of the Polyakov loop inside the topological clusters and the(model-dependent) accumulated topological cluster charges support this interpretation. Above thedeconfining phase transition light dyons (according to Kraan-van Baal caloron solutions with almosttrivial holonomy) become the most abundant topological objects. They are presumably responsiblefor the magnetic confinement in the deconfined phase.

We calculate the in-medium $D$ meson self-energies in a hot pion gas induced by resonance interactions with pions. The appropriate resonances in the {\it s},~ {\it p} and {\it d} waves of the $D$ meson-pion pair are represented by low lying scalar, vector and tensor $D^*$ mesons. At temperatures around 200 MeV the D-meson mass drops by $30~ \rm {MeV}$ and the scattering width grows up to $60~ \rm {MeV}$. Similar medium effects are found for the $D^*$ vector mesons. This opens and/or enhances the decay and/or dissociation channels of the charmonium states $\Psi^\prime$, $\chi_c$ and $J/\Psi$ to $D \bar D,~D^* \bar D,~D \bar D^* ,~D^* \bar D^*$ pairs in pion matter., Comment: 5 pages Revtex, 4 eps figures, final version accepted for publication in PRC

We report on our search for Kraan-van Baal calorons in finite temperature SU(2) lattice ensembles. We also discuss recent progress made in developing a caloron-anticaloron gas model decribing confinement and deconfinement in the context of trivial and non-trivial holonomy.

Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of $SU(2)$ lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analyzing their monopole content according to the Polyakov gauge and the maximally Abelian gauge, we characterize part of them to correspond to nonstatic calorons or static dyons in the context of Kraan-van Baal caloron solutions with nontrivial holonomy. The behavior of the Polyakov loop inside these clusters and the (model-dependent) topological charges of these objects support this interpretation.

We consider the {theta}{sup +}(1540) pentaquark in the string model that correctly reproduces the linear Regge trajectories for the case of orbtal excitations of light qq mesons and qqq baryons. Assuming (and arguing in favor of) the diquark-antiquark-diquark ([ud]s[ud]) clustering of this orbitally excited object we found its mass about 290 MeV above the experimental value 1540 MeV. In the model considered this discrepancy could be attributed to the change of the constituent mass of s antiquark as compared to that of s quark localized at the string end.

The mean field (MF) approximation for the pion matter, being equivalent to the leading ChPT order, involves no dynamical loops and, if self-consistent, produces finite renormalizations only. The weight factor of the Haar measure of the pion fields, entering the path integral, generates an effective Lagrangian $\delta \mathcal{L}_{H}$ which is generally singular in the continuum limit. There exists one parameterization of the pion fields only, for which the weight factor is equal to unity and $\delta \mathcal{L}_{H}=0$, respectively. This unique parameterization ensures selfconsistency of the MF approximation. We use it to calculate thermal Green functions of the pion gas in the MF approximation as a power series over the temperature. The Borel transforms of thermal averages of a function $\mathcal{J}(\chi ^{\alpha}\chi ^{\alpha})$ of the pion fields $\chi ^{\alpha}$ with respect to the scalar pion density are found to be $\frac{2}{\sqrt{\pi}}\mathcal{J}(4t)$. The perturbation series over the scalar pion density for basic characteristics of the pion matter such as the pion propagator, the pion optical potential, the scalar quark condensate $$, the in-medium pion decay constant ${\tilde{F}}$, and the equation of state of pion matter appear to be asymptotic ones. These series are summed up using the contour-improved Borel resummation method. The quark scalar condensate decreases smoothly until $T_{max}\simeq 310$ MeV. The temperature $T_{max}$ is the maximum temperature admissible for thermalized non-linear sigma model at zero pion chemical potentials. The estimate of $T_{max}$ is above the chemical freeze-out temperature $T\simeq 170$ MeV at RHIC and above the phase transition to two-flavor quark matter $T_{c} \simeq 175$ MeV, predicted by lattice gauge theories., Comment: Replaced with revised and extended version. Results are compared to lattice gauge theories. 16 pages REVTeX, 13 eps figures

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic-field configurations were left over after the annihilation of constituents that formed metastable $Q=0$ configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently nontrivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic-field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations.

By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge theory it has been shown that topological objects (calorons) observed on the lattice in the confined phase possess a dyonic substructure which becomes visible under certain circumstances. Here we show that, with decreasing temperature of the equilibrium ensemble, the distribution in the caloron parameter space is modified such that the calorons appear non-dissociated into constituent dyons. Still the calorons have nontrivial holonomy which is demonstrated by the Polyakov line behaviour for these configurations. At vanishing temperature (on a symmetric lattice) topological lumps obtained by cooling possess rotational symmetry in 4D and a characteristic double peak structure of Polyakov lines (defined with respect to temporal and spatial directions) with non-trivial asymptotics.

Finite temperature Euclidean SU(2) lattice gauge fields close to the deconfinement phase transition are subjected to cooling. We find relatively stable or absolutely stable configurations with an action below the one-instanton action $S_{inst}=2\pi^2$ both in the deconfinement and the confinement phases. In this paper we attempt an interpretation of these lowest action configurations. Their action is purely magnetic and amounts to $S/S_{inst} \approx N_t/N_s$, where $N_t$ ($N_s$) is the timelike (spacelike) lattice size, while the topological charge vanishes. In the confined phase part of the corresponding lattice configurations turns out to be absolutely stable with respect to the cooling process in which case Abelian projection reveals a homogeneous, purely Abelian magnetic field closed over the "boundary" in one of the spatial directions. Referring to the dyonic structure established for the confinement phase near $T_c$ and based on the observation made for this phase that such events below the instanton action $S_{inst}$ emerge from dyon-antidyon annihilation, the question of stability (metastability) is discussed for both phases. The hypothetically different dyonic structure of the deconfinement phase, inaccessible by cooling, could explain the metastability., Comment: 14 pages, 7 figures

We report the observation of calorons with nontrivial holonomy and fractional topological charge objects in cooled lattice samples derived from SU(2) equilibrium ensembles at $T, Comment: 3 pages, 3 figures, talk given at Confinement V, Gargnano, Italy, 10-14 Sep 2002. References and acknowlegements added

We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical Yang-Mills equations with temperature in the context of SU(3) lattice gauge theory. We present discretized lattice versions of KvBLL solutions and other dyonic structures, obtained by cooling in order to understand their variety and signature. An analysis of the zero modes of the lattice Dirac operator for different fermionic boundary conditions gives clear evidence for a KvBLL-like background of finite T lattice subensembles with Q = +/-1. Using APE-smearing we are able to study the topological charge density q(x) of the configurations and to corroborate this interpretation., Comment: Presented at LATTICE 2003 (topology) by C. Gattringer and E.M. Ilgenfritz, 6 pages

Finite temperature Euclidean SU(2) lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilson-fermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.

With the help of the cooling method applied to SU(2) lattice gauge theory at non-zero $T \le T_c$ we present numerical evidence for the existence of superpositions of Kraan-van Baal caloron (or BPS monopole pair) solutions with non-trivial holonomy, which might constitute an important contribution to the semi-classical approximation of the partition function., Comment: 3 pages, 6 figures, contribution to Lattice2002(topology)

The field strength correlators at zero temperature are semi-classically evaluated fitting the random instanton liquid model to lattice data for quenched SU(3) lattice gauge theory. We restrict ourselves to the lowest order in an instanton density expansion necessary to explain the difference between transverse and longitudinal correlation functions. In the instanton-instanton and instanton-antiinstanton contributions the Schwinger line factors neglected in a previous analysis are numerically taken into account in a weighted Monte Carlo evaluation. This leads to different estimates for instanton size and density. A reasonable description of the correlators within the intermediate range from 0.4 fm to 1 fm is obtained., 20 pages, 3 figures

We study SU(2) lattice gauge theory at $T>0$ in a finite box with fixed holonomy value at the spatial boundary. We search for (approximate) classical solutions of the lattice field equations and find in particular the dissociated calorons recently discussed by van Baal and collaborators., Talk at Lattice 2000, Bangalore; 4 pages, 4 figures, LaTeX

Low temperature of the phase transition into the quark-gluon plasma correspond to low values of the bag model constant and to absolutely stable strange quark matter. Some of the observed pulsars are identified quite reliably as neutron stars. If strange matter is stable, the central density of these pulsars is to be smaller that critical density of the phase transition into the nonstrange quark matter. The nonstrange quark matter being formed turns to more stable strange matter on a weak interaction timescale converting neutron stars into strange stars. The requirement of stability of old and newly born neutron stars is used to constrain the bag model constant and the critical temperature of the phase transition into the quark-gluon plasma at zero chemical potential.

Field strength correlators are semi-classically evaluated in the dilute gas model of non-Abelian sources (instantons) and compared with lattice data for QCD at zero temperature. We show that one of the Euclidean invariant, tensorial structures vanishes for configurations being purely selfdual or anti-selfdual. We compute the invariant functions contributing to the correlators within the two lowest orders in an instanton density expansion. Fitting instanton size and density for quenched and full QCD, we obtain a reasonable description., 29 pages (revtex) including 3 figures, revised for publication in Phys. Rev. D