The rotation effect on the QCD properties is an open question. We study the dynamic gluon mass in a dense QCD matter, the rotation is introduced by taking a covariant transformation between the flat and curved spaces. The law of causality which restricts the rotation strength of the system is carefully considered in the calculation. We find that the rotation effect is not monotonous. Overall, it behaves like an anti-screening effect, reflecting in the decreasing gluon mass, but the strength changes with the rotation. For a QCD matter with low baryon density, the screening effect in the flat space can be completely canceled by the rotation, and gluons are confined in a strongly rotating matter. When the rotation is extremely high, the matter approaches to a weakly interacting gas.

China

Guojun Huang

Shile Chen

Yin Jiang

Germany

Jiaxing Zhao

Pengfei Zhuang

Rotation induced color confinement

In this paper, we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks (ANNs). The actions are estimated by learning system configurations governed by the Boltzmann factor,   $ e^{-S} $  , at different temperatures within the imaginary time formalism of thermal field theory. Specifically, we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method. Continuous-mixture autoregressive networks (CANs) enable the construction of accurate effective actions with tractable probability density estimation. Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles. This capability is especially valuable for detailed exploration of phase diagrams.

Tian Xu

Lingxiao Wang

Lianyi He

Hong Kong

Kai Zhou

Building imaginary-time thermal field theory with artificial neural networks  

In this work a non-abelian gauge theory is reformulated in a rotating frame. With this new formalism, the influence of the background rotation on the color deconfinement transition for a pure SU(2) gluon system has been studied. The KvBLL caloron, which is a color neutral and topologically nontrivial solution of Yang-Mills equation at finite temperature, is reexamined under rotation and adopted as the confined vacuum of such a system. With rotation-modified solutions of the caloron's constituent solitons, i.e. dyons, the non-perturbative part of effective potential of the rotating system has been obtained. Combining with the perturbative potential by Gaussian fluctuations, the critical temperature of confinement-deconfinement phase transition is investigated. It is found that neither the rotational semi-classical potential nor Gaussian fluctuations can confine color charges more tightly when the rotation becomes faster. While only a stronger coupling constant is able to make the critical temperature increase with angular velocity, as what indicated in lattice simulations. And it is found a non-monotonic dependence of the critical temperature on the angular velocity is established because of the competition between these two contrary contributions.

Rotating SU(2) gluon matter and deconfinement at finite temperature

Gluon interaction introduces remarkable corrections to the magnetic polarization effects on the chiral fermions, which is known as the inverse magnetic catalysis. It is a natural speculation that the vorticity, which has many similar properties as magnetic field, would bring non-negligible contribution to the chiral rotational suppression. Using an intuitive semi-classical background field method we studied the rotation dependence of the effective strong interaction coupling constant. Contrary to the magnetic field case the rotation increases the effective coupling which would slow down the condensate melting with temperature. This could be named as the chiral vortical catalysis or inverse rotation suppression. Imposing such dependence on the 4-fermion coupling in the NJL model, we numerically checked this analysis qualitatively. The pseudo critical temperature is shown to rise with the rotation and approach saturation eventually which may be induced by the model cutoff.

Chiral vortical catalysis

A strong background field drastically changes the vacuum structure and proper basis of a system in both classical and quantum mechanics, e.g., the Landau levels in a background magnetic field. This is true even for a rotating system. In such a system, the usual set of plane-wave states would no longer be suitable as a starting point of perturbation. Alternatively and straightforwardly, in a rapidly and globally rotating system, it is better to reformulate the perturbation computation in principle. In this study, we completed the first step for the spin-1 field, which includes solving the Proca equation in the presence of a background rotation and completing its canonical quantization. We show that because of the symmetry, the eigen states are actually the same as those of Maxwell equations in cylindrical coordinates. The propagator as well as the near-central approximation were obtained by assuming that the vorticity areas are very small in the relativistic QGP.

Proca equation and vector field quantization in a rotating system  

In this work, the existence of Borromean states is discussed for bosonic and fermionic cases in both the relativistic and non-relativistic limits from the 3-momentum shell renormalization. With the linear bosonic model, we check the existence of Efimov-like states in the bosonic system. In both limits a geometric series of singularities is found in the 3-boson interaction vertex, while the energy ratio is reduced by around 70% in the relativistic limit because of the anti-particle contribution. Motivated by the quark-diquark model in heavy baryon studies, we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale. This may indicate a special baryonic state of light quarks in high energy quark matter. In other cases, trivial results are obtained as expected. In the relativistic limit, for both bosonic and fermionic cases, potential Borromean states are independent of the mass, which means the results would also be valid even in the zero-mass limit.

Ziyue Wang

Shao-Jian Jiang

Relativistic Borromean states  

We study the confinement phase transition in SU(2) Yang-Mills theory, based on a statistical ensemble model of correlated instanton-dyons. We show for the first time that such a model provides a quantitative description, in light of the lattice data, for the temperature dependence of the order parameter. We characterize the short-range interaction which plays a crucial role for the properties of such an ensemble. The chromomagnetic charge density as well as the spatial correlations are found to be consistent with known lattice and phenomenological information.

United States

Miguel Angel Lopez-Ruiz

Jinfeng Liao

Confinement from correlated instanton-dyon ensembles in SU(2) Yang-Mills theory

Recently, there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system that is generally out of equilibrium is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up to <math><mrow><mover><mrow><mi>O</mi></mrow><mrow><mo>^</mo></mrow></mover><mo>(</mo><mo>ℏ</mo><mo>)</mo></mrow></math> order. In particular, we clarify certain subtle and confusing issues surrounding the Lorentz noninvariance and frame dependence associated with the three-dimensional chiral kinetic theory. We prove that such frame dependence is uniquely and completely fixed by an unambiguous definition of the <math><mrow><mover><mrow><mi>O</mi></mrow><mrow><mo>^</mo></mrow></mover><mo>(</mo><mo>ℏ</mo><mo>)</mo></mrow></math> correction to the distribution function in each reference frame.

Anping Huang

Shuzhe Shi

Complete and consistent chiral transport from Wigner function formalism

The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromomagnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (nonsupersymmetric) theories. Recently, a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective “Higgsing” mechanism. We report a thorough numerical investigation of the confinement dynamics in <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.

Confinement, holonomy, and correlated instanton-dyon ensemble: SU(2) Yang-Mills theory

Recently there has been significant interest in the macroscopic manifestation of chiral anomaly in many-body systems of chiral fermions. A notable example is the Chiral Magnetic Effect (CME). Enthusiastic efforts have been made to search for the CME in the quark-gluon plasma created in heavy ion collisions. A crucial challenge is that the extremely strong magnetic field in such collisions may last only for a brief moment and the CME current may have to occur at so early a stage that the quark-gluon matter is still far from thermal equilibrium. This thus requires modeling of the CME in an out-of-equilibrium setting. With the recently developed theoretical tool of chiral kinetic theory, we make a first phenomenological study of the CME-induced charge separation during the pre-thermal stage in heavy ion collisions. The effect is found to be very sensitive to the time dependence of the magnetic field and also influenced by the initial quark momentum spectrum as well as the relaxation time of the system evolution toward thermal equilibrium. Within the present approach, such pre-thermal charge separation is found to be modest.