Domain wall network as QCD vacuum and the chromomagnetic trap formation under extreme conditions

Abstract

The ensemble of Euclidean gluon field configurations represented by the domain wall network is considered. A single domain wall is given by the sine-Gordon kink for the angle between chromomagnetic and chromoelectric components of the gauge field. The domain wall separates the regions with self-dual and anti-self-dual fields. The network of the domain wall defects is introduced as a combination of multiplicative and additive superpositions of kinks. The character of the spectrum and eigenmodes of color-charged fluctuations in the presence of the domain wall network is discussed. The concept of the confinement-deconfinement transition in terms of the ensemble of domain wall networks is outlined. Conditions for the formation of a stable thick domain wall junction (the chromomagnetic trap) during heavy ion collisions are discussed, and the spectrum of color charged quasiparticles inside the trap is evaluated. An important observation is the existence of the critical size Lc of the trap stable against gluon tachyonic modes, which means that deconfinement can occur only in a finite region of space-time in principle. The size Lc is related to the value of gluon condensate g 2 F 2 .

Finite Size Effects in the Free Energy Density for Abelian (Anti-)Self-Dual Gluon Field in SU(3) Gluodynamics

“…V R is the four-dimensional spherical region with boundary ∂V R . Justification of this choice for the boundary conditions can be found in [9,13]. The normalization N is chosen in such a way that the effective potential is equal to zero at vanishing background field strength.…”

Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

“…As it has already been mentioned in Introduction, nonperturbative calculation of QCD quantum effective action within the functional renormalization group approach [19] supported the one-loop result [14,16,17] and indicated the existence of a minimum of the effective potential for nonzero value of Abelian (anti-)self-dual homogeneous gluon field. Ginzburg-Landau (GL) approach to the quantum effective action indicated a possibility of the domain wall network formation in QCD vacuum resulting in the dominating vacuum gluon configuration seen as an ensemble of densely packed lumps of covariantly constant Abelian (anti-)self-dual field [9,12,20,21]. Nonzero scalar gluon condensate g 2 F a µν F a µν postulated by the effective potential leads to the existence of twelve discrete degenerate global minima of the effective action (see Fig.1),…”

“…The minima in the dark gray regions correspond to the Abelian (anti-)self-dual configurations and form a periodic structure labelled by integer indices (kl) in Eq. (1) (for more details see [9,12,20]). …”

“…The model of hadronization developed in [7,8,12,13] indicated that the spectrum of mesons displayed the Regge character both with respect to total angular momentum and radial quantum number of the meson. The reason for confinement of a single quark and Regge spectrum of mesons turned out to be the same -the analytic properties of quark and gluon propagators.…”

Influence of confining gluon configurations on the P→γ*γ transition form factors

“…In this paper we consider behaviour of the transition form factors within the approach based on the description of QCD vacuum as statistical ensemble of domain wall networks representing an ensemble of almost everywhere homogeneous Abelian (anti-)self-dual fields, which are characterized by the nonzero gluon condensates, first of all the scalar g 2 F 2 and the absolute value of the pseudoscalar |g 2F F | = g 2 F 2 ones. Motivation for this approach as well as details related to the study of static and dynamical confinement, realization of chiral SU L (N f ) × SU R (N f ) and U A (1) symmetries in terms of quark-gluon as well as colorless hadron degrees of freedom can be found in papers [32][33][34][35][36][37] and references therein. The effective meson action derived in the model allows one to compute the mass spectrum, decay and transition constants as well as form factors describing the strong, electromagnetic and weak interactions of various mesons.…”