arXiv subjects
Publications and source records attributed to V. Chelnokov.
We present results for the chromo-electric field generated by a static quark-antiquark pair at nearly zero temperature in lattice QCD with 2+1 dynamical staggered fermions at physical quark masses. We investigate the evolution of the flux-tube structure as the distance between the static color charges increases. We find hints that string breaking occurs at a distance in the range $0.963 \; \text{fm} \; \lesssim \; d^* \lesssim \; 1.156 \; \text{fm}$.
We present a study of the structure of the chromoelectrical field created by a static quark-antiquark pair in lattice QCD with 2+1 flavours of dynamical quarks, where the quark masses are set to their physical values. The analysis covers a wide range of temperatures both above and below the chiral crossover, and explores varying quark-antiquark distances, with the aim of identifying signals of deconfinement and string breaking in the field structure. To this end we apply the zero-curl perturbative field subtraction method, developed in our earlier studies of pure gauge SU(3) theory and of full QCD at zero temperature.
We explore the possibility to use the Fredenhagen-Marcu operator as a candidate order parameter of the deconfinement phase transition in gauge matter systems at finite temperature. Concretely, we compute by numerical simulations this operator in the (2+1)-dimensional Z(2) lattice gauge theory (LGT) with Z(2) gauge fields coupled to Z(2)-valued Higgs fields. While we cannot provide an unambiguous evidence, we present some hints that the Fredenhagen-Marcu operator is capable of distinguishing the deconfinement phase from the Higgs and confinement phases of the theory.
An exact solution of one-dimensional lattice gauge theory at finite temperature and non-zero chemical potential is reviewed for the gauge groups $G=Z(N),U(N),SU(N)$ for all values of $N$ and the number of fermion flavors $N_f$. Calculated are the partition function, free energy, the Polyakov loop expectation values, baryon density, quark condensate, meson and baryon correlation functions. Detailed analysis of the exact solutions is done for $N=2,3$ with one and two fermion flavors. In the large $N_f$ limit we uncover the Roberge-Weiss phase transition and discuss its remnants at finite $N_f$. In the case of $N_f$ degenerate flavors we also calculate 1) the large $N$ limit, 2) the large $N_f$ limit and 3) the 't Hooft-Veneziano limit of all models. The critical behavior of the models in these limits is studied and the phase structure is described in details. A comparison of all limits with $U(3)$ and $SU(3)$ QCD is also performed. In order to achieve these results we explore several representations of the partition function of one-dimensional QCD obtained and described in the text.
We present lattice Monte Carlo results on the chromoelectric field created by a static quark-antiquark pair in the vacuum of QCD with 2+1 dynamical staggered fermions at physical masses. After isolating the nonperturbative, confining part of the field, we characterize its spatial profile for several values of the physical distances between the sources, ranging from about 0.5 fm up to the onset of string breaking. Moreover, we compare our results with a model of QCD vacuum as disordered chromomagnetic condensate.
We explore the 't Hooft-Veneziano limit of the Polyakov loop models at finite baryon chemical potential. Using methods developed by us earlier we calculate the two- and $N$-point correlation functions of the Polyakov loops. This gives a possibility to compute the various potentials in the confinement phase and to derive the screening masses outside the confinement region. In particular, we establish the existence of complex masses and an oscillating decay of correlations in a certain range of parameters. Furthermore, it is shown that the calculation of the $N$-point correlation function in the confinement phase reduces to the geometric median problem. This leads to a large $N$ analog of the $Y$ law for the baryon potential.
We report on the results of measuring the chromoelectric fields in a flux tube created by a static quark-antiquark pair in the finite-temperature SU(3) gauge theory. Below the deconfinement temperature the field behavior is similar to the zero-temperature case. Above the deconfinement temperature the field shape remains the same, but the field values drop when the distance between quark and antiquark increases, thus showing the disappearance of confining potential.
Computations of screening masses in finite-temperature QCD at finite density are plagued by the sign problem and have been performed so far with an imaginary chemical potential. Here, we use a dual formulation of a Polyakov-loop model which allows the determination of screening masses at real baryon chemical potential. This is a second paper in a series devoted to a detailed study of dual Polyakov-loop models at finite density. While the first paper was mainly devoted to establishing the phase diagram of the model, here we compute correlation functions of the Polyakov loops and the second-moment correlation length at non-zero chemical potential. This enables us to evaluate numerically the screening masses from correlations of the real and imaginary parts of the Polyakov loops. We also compute these masses in the mean-field approximation and compare with numerical results. In addition, we provide a quantitative improvement of the general phase diagram presented in the first paper.
A characteristic signature of quark confinement is the concentration of the chromoelectric field between a static quark-antiquark pair in a flux tube. However, the structure of this flux tube, and hence of the confining force, has not been completely understood. Here we perform new lattice measurements of field distributions on smeared Monte Carlo ensembles in SU(3) gauge theory. On the basis of these simulations we demonstrate that the confining force can be understood using the analogy with the basic principles of electromagnetism as elucidated by Maxwell. We derive a chromomagnetic Lorentz force density coupling the chromoelectric field to chromomagnetic currents and integrate this force density over the flux tube interior to obtain a Maxwell-like force that squeezes the flux tube in the transverse direction. We show that the strength of this transverse confining force is equal to the value of the string tension calculated numerically from the chromoelectric field on the midplane between the quarks, verifying the consistency of these two complementary pictures of confinement.
Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number of fermion flavors and in any dimension. The distinguished feature of the dual formulation is that the dual Boltzmann weight is strictly positive. This allows to gain reliable results at finite density via the Monte Carlo simulations. As a byproduct of the dual representation we outline an exact solution for the partition function of the (1 + 1)-dimensional theory and reveal an existence of a phase with oscillating correlations.
The broad class of U(N) and SU(N) Polyakov loop models on the lattice are solved exactly in the combined large N, Nf limit, where N is a number of colors and Nf is a number of quark flavors, and in any dimension. In this 't Hooft-Veneziano limit the ratio N/Nf is kept fixed. We calculate both the free energy and various correlation functions. The critical behavior of the models is described in details at finite temperatures and non-zero baryon chemical potential. Furthermore, we prove that the calculation of the N-point (baryon) correlation function reduces to the geometric median problem in the confinement phase. In the deconfinement phase we establish an existence of the complex masses and an oscillating decay of correlations in a certain region of parameters.
We measure the spatial distribution of all components of the color fields surrounding a static quark antiquark pair in QCD with (2+1) HISQ flavors. We isolate the nonperturbative component of the longitudinal chromoelectric color field responsible for the linear term in the confining potential.
The 't Hooft-Veneziano limit of various U(N) and SU(N) Polyakov loop models is constructed at finite temperature and non-zero baryon chemical potential. In this paper we calculate the free energy, its derivatives, the Polyakov loop expectation values and the baryon density. The phase diagram is described in details.
The standard U(N) and SU(N) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of SU(N) models and discuss implications of our results for the large N behaviour of SU(N) lattice gauge theories at finite temperatures and non-zero baryon chemical potential. The key ingredients of our approach are 1) expansion of the integrals into a sum over irreducible representations and 2) calculation of sums over partitions of r of products of dimensions of two different representations of a symmetric group $S_r$.
Dual representations are constructed for non-abelian lattice spin models with U(N) and SU(N) symmetry groups, for all N and in any dimension. These models are usually related to the effective models describing the interaction between Polyakov loops in the strong coupled QCD. The original spin degrees of freedom are explicitly integrated out and a dual theory appears to be a local theory for the dual integer-valued variables. The construction is performed for the partition function and for the most general correlation function. The latter include the two-point function corresponding to quark-anti-quark free energy and the N-point function related to the free energy of a baryon. We consider both pure gauge models and models with static fermion determinant for both the staggered and Wilson fermions with an arbitrary number of flavours. While the Boltzmann weights of such models are complex in the presence of non-zero chemical potential the dual Boltzmann weights appear to be strictly positive on admissible configurations. An essential part of this work with respect to previous studies is an extension of the dual representation to the case of 1) an arbitrary value of the temporal coupling constant in the Wilson action and 2) an arbitrary number of flavours of static quark determinants. The applications and extensions of the results are discussed in detail. In particular, we outline a possible approach to Monte-Carlo simulations of the dual theory, to the large N expansion and to the development of a tensor renormalization group.
We extend a previous numerical study of SU(3) Yang-Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark-antiquark pair for a wide range of quark-antiquark separations, and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like 'perturbative' field and a 'non-perturbative' field, identified as the confining part of the SU(3) flux tube field. In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string tension. Under this assumption the string tension is determined by the color fields we measure, which form a tensor $F_{μν}$ pointing in a single direction in color space. We call this the Maxwell mechanism of confinement. We provide an additional procedure to isolate the non-perturbative (confining) field. We then extract the string tension from a stress energy-momentum tensor $T_{μν}$ having the Maxwell form, constructed from the non-perturbative part of the tensor $F_{μν}$ obtained from our simulations. To test our hypothesis we calculate the string tension from our simulations of the color fields for ten values of the quark-antiquark separation ranging from 0.37 fm to 1.2 fm. We also calculate the spatial distributions of the energy-momentum tensor $T_{μν}$ surrounding static quarks for this range of separations, and we compare these distributions with those obtained from direct simulations of the energy-momentum tensor in SU(3) Yang-Mills theory.
Using lattice Monte Carlo simulations of SU(3) pure gauge theory, we determine the spatial distribution of all components of the color fields created by a static quark and antiquark. We identify the components of the measured chromoelectric field transverse to the line connecting the quark-antiquark pair with the transverse components of an effective Coulomb-like field $\vec{E}^C $ associated with the quark sources. Subtracting $\vec{E}^C$ from the total simulated chromoelectric field $\vec{E}$ yields a non-perturbative, primarily longitudinal chromoelectric field $\vec{E}^{NP}$, which we identify as the confining field. This is the first time that the chromoelectric field has been separated into perturbative and nonperturbative components, creating a new tool to study the color field distribution between a quark and an antiquark, and thus the long distance force between them.
Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $Δ$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $q\bar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.