The temperature of the chiral restoration phase transition at 130 MeV as well as the temperature of the center symmetry (deconfinement) phase transition in a pure glue theory at 300 MeV are two independent temperatures and their interplay determines
a structure of different regimes of hot QCD. Given a chiral spin symmetry of the color charge and of the chromoelectric interaction we can conclude from observed symmetries of spatial and temporal correlators of N_F=2 QCD with domain wall Dirac operator at physical quark masses that above the chiral symmetry restoration crossover around T_pc but below rougly 3T_pc there should exist an intermediate regime (the stringy fluid) of hot QCD that is characterized by approximate chiral spin symmetry and where degrees of freedom are chirally symmetric quarks bound into color singlet objects by the chromoelectric field. Above this intermediate regime the color charge and the chromoelectric field are Debye screened and one observes a transition to QGP with magnetic confinement.
Above the pseudocritical temperature T_c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At
the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined.
Above a pseudocritical temperature of chiral symmetry restoration T_c the energy and the pressure are very far from the quark-gluon-plasma limit (i.e. ideal gas of free quarks and gluons). At the same time very soon above T_c fluctuations of conserve
d charges behave as if quarks were free particles. Within the T_c - 3T_c interval a chiral spin symmetry emerges in QCD which is not consistent with free quarks and suggests that degrees of freedom are chirally symmetric quarks bound into the color-singlet objects by the chromoelectric field. Here we analyse temporal and spatial correlators in this interval and demonstrate that they indicate simultaneously the chiral spin symmetry as well as absence of the interquark interactions in channels constrained by a current conservation. The latter channels are responsible for both fluctuations of conserved charges and for dileptons. Assuming that a SU(2)_color subgroup of SU(3)_color is deconfined soon above T_c but confinement persits in SU(3)_color/SU(2)_color in the interval T_c - 3T_c we are able to reconcile all empirical facts listed above.
The chiral magnetic effect (CME) is an exact statement that connects via the axial anomaly the electric current in a system consisting of interacting fermions and gauge field with chirality imbalance that is put into a strong external magnetic field.
Experimental search of the magnetically induced current in QCD in heavy ion collisions above a pseudocritical temperature hints, though not yet conclusive, that the induced current is either small or vanishing. This would imply that the chirality imbalance in QCD above $T_c$ that could be generated via topological fluctuations is at most very small. Here we present the most general reason for absence (smallness) of the chirality imbalance in QCD above Tc. It was recently found on the lattice that QCD above Tc is approximately chiral spin (CS) symmetric with the symmetry breaking at the level of a few percent. The CS transformations mix the right- and left-handed components of quarks. Then an exact CS symmetry would require absence of any chirality imbalance. Consequently an approximate CS symmetry admits at most a very small chirality imbalance in QCD above Tc. Hence the absence or smallness of an magnetically induced current observed in heavy ion collisions could be considered as experimental evidence for emergence of the CS symmetry above Tc.
In his recent Comments E. Shuryak reiterates old, unfortunately misleading arguments in favor of deconfined Quark-Gluon Plasma (QGP) immediately above the chiral restoration pseudocritical temperature. In a Comment devoted to our view of QCD at high
temperatures he does not address and even mention the essence of our arguments. In recent years a new hidden symmetry in QCD was discovered. It is a symmetry of the electric sector of QCD, that is higher than the chiral symmetry of the QCD Lagrangian as the whole. This symmetry was clearly observed above T_c in spatial correlators and very recently also in time correlators. The latter correlators are directly related to observable spectral density. Then in a model-independent way we conclude that degrees of freedom in QCD above T_c, but below roughly 3T_c, are chirally symmetric quarks bound by the chromoelectric field into color-singlet compounds without the chromomagnetic effects. This regime of QCD has been referred to as a Stringy Fluid since such objects are very reminiscent of strings.At higher temperatures there is a very smooth transition to the partonic degrees of freedom, i.e. to the QGP regime. Here we will address some of the points made by Shuryak.
Recently, via calculation of spatial correlators of $J=0,1$ isovector operators using a chirally symmetric Dirac operator within $N_F=2$ QCD, it has been found that QCD at temperatures $T_c - 3 T_c$ is approximately $SU(2)_{CS}$ and $SU(4)$ symmetric
. The latter symmetry suggests that the physical degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color singlet objects without chromomagnetic effects. This regime of QCD has been referred to as a Stringy Fluid. Here we calculate correlators for propagation in time direction at a temperature slightly above $T_c$ and find the same approximate symmetries. This means that the meson spectral function is chiral-spin and $SU(4)$ symmetric.
While the QCD Lagrangian as the whole is only chirally symmetric, its electric part has larger chiral-spin SU(2)_{CS} and SU(2N_F) symmetries. This allows separation of the electric and magnetic interactions in a given reference frame. Artificial tru
ncation of the near-zero modes of the Dirac operator results in the emergence of the SU(2)_{CS} and SU(2N_F) symmetries in hadron spectrum. This implies that while the confining electric interaction is distributed among all modes of the Dirac operator, the magnetic interaction is located at least predominantly in the near-zero modes. Given this observation one could anticipate that above the pseudocritical temperature, where the near-zero modes of the Dirac operator are suppressed, QCD is SU(2)_{CS} and SU(2N_F) symmetric, which means absence of deconfinement in this regime. Solution of the N_F=2 QCD on the lattice with a chirally symmetric Dirac operator reveals that indeed in the interval Tc - 3Tc QCD is approximately SU(2)_{CS} and SU(2N_F) symmetric which implies that degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color-singlet objects without the chromomagnetic effects. This regime is referred to as a Stringy Fluid. At larger temperatures this emergent symmetry smoothly disappears and QCD approaches the Quark-Gluon Plasma regime with quasifree quarks. The Hadron Gas, the Stringy Fluid and the Quark-Gluon Plasma differ by symmetries, degrees of freedom and properties.
In a local gauge-invariant theory with massless Dirac fermions a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge o
perator is invariant under a larger symmetry group, SU(2N_F), that includes chiral transformations as well as SU(2)_{CS} chiralspin transformations that mix the right- and left-handed components of fermions. Consequently a symmetry of the electric interaction, that is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows to separate in some situations electric and magnetic contributions. In particutar, in QCD the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate SU(2)_{CS} and SU(2N_F) symmetries that are incompatible with free deconfined quarks. Consequently elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime QCD can be described as a stringy fluid.
The chirally symmetric baryon parity-doublet model can be used as an effective description of the baryon-like objects in the chirally symmetric phase of QCD. Recently it has been found that above the critical temperature higher chiralspin symmetries
emerge in QCD. It is demonstrated here that the baryon parity-doublet Lagrangian is manifestly chiralspin-invariant. We construct nucleon interpolators with fixed chiralspin transformation properties that can be used in lattice studies at high T.
We identify the chiral and angular momentum content of the leading quark-antiquark Fock component for the $rho(770)$ and $rho(1450)$ mesons using a two-flavor lattice simulation with dynamical Overlap Dirac fermions. We extract this information from
the overlap factors of two interpolating fields with different chiral structure and from the unitary transformation between chiral and angular momentum basis. For the chiral content of the mesons we find that the $rho(770)$ slightly favors the $(1,0)oplus(0,1)$ chiral representation and the $rho(1450)$ slightly favors the $(1/2,1/2)_b$ chiral representation. In the angular momentum basis the $rho(770)$ is then a $^3S_1$ state, in accordance with the quark model. The $rho(1450)$ is a $^3D_1$ state, showing that the quark model wrongly assumes the $rho(1450)$ to be a radial excitation of the $rho(770)$.
