arXiv subjects

L. Ya. Glozman

Publications and source records attributed to L. Ya. Glozman.

At least 19 recordsLinked to original sources

arXiv2026

Why fluctuations of conserved charges in the confining regime above $T_{ch}$ behave as if the quarks were free?

Some cumulants of the fluctuations of conserved charges soon above the chiral crossover behave as if the quarks were free. This was taken by many as evidence of deconfinement. At the same temperatures the mesonic correlators reveal the chiral spin and SU(4) symmetries, indicating that the propagating degrees of freedom are massless quarks connected into color singlets by the chromoelectric confining string. These correlators are qualitatively different from the free quark gas. Here we clarify the reason for the difference. The conserved quark number densities do not propagate in time but do propagate in spatial directions. The mesonic propagators calculated in full QCD differ radically from the free quark loop (quark gas) above T_ch. In contrast, the quark number density spatial propagator in full QCD at T > 220 MeV is very close to the free quark loop. In other words, the conserved charges do not see confinement, in contrast to the mesonic correlators. This is consistent with the well understood quark-hadron duality at T=0 in e^+e^- -> hadrons, where at invariant masses above 2 GeV the cross-section in the confining regime is represented by the free quark loop plus small perturbative corrections. All these features above T_ch but below the deconfinement temperature T_d can be combined within the following microscopic picture of the stringy fluid matter. It is a medium of the overlapping strongly interacting color singlet clusters. The quark interchanges between the clusters, required by Paili principle, make the quarks quasifree, which is reflected in fluctuations of conserved charges.

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arXiv2026

A large size of the pion-like excitations in the stringy fluid above $T_{ch}$ is model independent and required by current algebra

Multiple lattice evidences support the existence of a confining but chirally symmetric stringy fluid regime of QCD above the chiral symmetry restoration temperature at T_{ch} ~ 155 MeV. This regime is characterized by an approximate chiral spin symmetry and its extensions which means that the propagating excitations represent the chirally symmetric quarks connected into color singlets by the chromoelectric string. Clear π,π' peaks above T_{ch} were extracted on the lattice from the spatial and temporal correlators, which become broader with temperature and disappear roughly at $3T_{ch}$. The meson-like excitations above T_{ch} were studied within the manifestly confining and chirally symmetric model. It has been demonstrated that the chiral symmetry restoration in the confining regime happens because of Pauli blocking of the levels, required for the existence of the quark condensate, by the thermal quark excitation. The same Pauli blocking leads to a huge swelling of the low-spin mesons above T_{ch} which become infinitely large in the chiral limit. This property should be crucial for the explanation of the high collectivity and a very small mean-free path of the constituents above $T_{ch}$ seen experimentally. Here we demonstrate that the swelling of pions above T_{ch} is a model-independent effect required by current algebra.

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arXiv2026

Three regimes/phases of QCD at high T, their symmetries and N_c scaling

We review recent developments on the QCD phase diagram at small chemical potentials and increasing temperature. There are three regimes/phases in QCD which differ by symmetries, degrees of freedom and N_c scaling: the hadron gas below the chiral restoration temperature T_ch, the stringy fluid between T_ch and the deconfinement temperature T_d and the quark-gluon plasma above T_d.

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arXiv2025

On the origin of the $Nc^1$ scaling in the confined but chirally symmetric phase at high T

There is lattice evidence that the QCD matter above the chiral restoration temperature Tch and below the deconfinement temperature Td, called stringy fluid, is characterized by an approximate chiral spin symmetry, which is a symmetry of confinement in QCD with light quarks. The energy density, pressure and entropy density in the stringy fluid scale as Nc^1, which is in contrast to the Nc^0 scaling in the hadron gas and to the Nc^2 scaling in the quark-gluon plasma. Here we clarify the origin of the Nc^1 scaling. We employ a solvable field-theoretical large $N_c$ chirally symmetric and confining model. In vacuum the confining potential induces a spontaneous breaking of chiral symmetry. The mesons are spatially localized states of quarks and antiquarks. Still in the confining regime the system undergoes the chiral restoration phase transition at $T_{ch}$ because of Paili blocking of the quark levels required for the existence of the quark condensate, by the thermal excitation of quarks and antiquarks. The same Paili blocking leads to a delocalization of the color singlet low-spin meson-like states that become infinitely large in the chiral limit. Consequently the stringy fluid represents a very dense medium of the overlapping huge color-singlet low-spin quark-antiquark systems. The Bethe-Salpeter equation that determines the rest-frame excitation energies of the color-singlet quark-antiquark system is Nc-independent both in vacuum and in the medium in the confining regime. The excitation energy of the quark-antiquark color-singlet systems scales as Nc^0, i.e. as meson mass in vacuum. The Nc^1 scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.

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arXiv2025

Chiral spin symmetry

We review the chiral spin symmetry, which is a symmetry of the color charge and of the confining electric part of QCD. Observation of this symmetry in the vacuum upon truncation of the near-zero modes of the Dirac operator implies that the hadron mass in the light quark sector is not due to the quark condensate of the vacuum and that confinement and chiral symmetry breaking are not directly related. Observation of this symmetry above the chiral symmetry restoration crossover suggests that QCD is still in the confining regime with chirally symmetric quarks bound into the color-singlets by the confining electric field. This regime of QCD was called a stringy fluid. At a temperature T_d that is essentially above T_ch the chiral spin symmetry smoothly disappears suggesting that the confining electric field gets screened and one observes a very smooth crossover to the quark-gluon plasma. The three-regimes picture has been further substantiated by the analysis of the N_c scaling of the energy density, the pressure and the entropy density. In the hadron gas they scale as N_c^0, in the stringy fluid as N_c^1 and in the quark-gluon plasma as N_c^2. We have analyzed the fluctuations of conserved charges that scale as N_c^1 above T_ch thus indicating a transition from the hadron gas to the stringy fluid. When N_c gets sufficiently large the three-regimes picture transforms into the three-phases phase diagram. Finally we discuss a confining and chirally symmetric model in 3+1 dimensions. This model demonstrates the chiral symmetry restoration in the confining regime and a delocalization of the color-singlet quark-antiquark systems that become very large at T > T_ch. Consequently the stringy fluid matter is a very dense highly collective system of the overlapping very large color-singlet quark-antiquark "mesons" with a very small mean free path.

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arXiv2025

Confined but chirally and chiral spin symmetric hot matter

We investigate properties of the quark--antiquark mesons at zero and finite temperature in the framework of a solvable chirally symmetric quark model with linear confining potential. The interquark interaction in the model is reminiscent of that derived in Coulomb gauge QCD, with the string tension being the only model parameter. We demonstrate that while the confining interaction induces spontaneous breaking of chiral symmetry at T=0, chiral symmetry gets restored at a temperature Tch ~ 90 MeV for the string tension fixed to provide the phenomenological value of the quark condensate. This temperature is similar to Tch ~ 130 MeV observed on the lattice in the chiral limit for N_c=3. The physical mechanism responsible for the chiral symmetry restoration in the confining regime is Pauli blocking of the quark levels, required for the existence of a nonvanishing quark condensate, by the thermal excitations of the quarks and antiquarks. Thus, above the chiral restoration temperature, the meson-like states are chirally symmetric and approximately chiral spin symmetric. A crucial property of the confined meson-like light-light states above Tch is their size that exceeds drastically that in the chirally broken phase below Tch, in contrast to the heavy-heavy mesons that nearly preserve their size irrespective of the temperature. This property is a result of Pauli blocking of the quark and antiquark levels with small momenta. Furthermore, the root-mean-square radius of the states with J=0,1 diverges in the chiral limit. This unexpected property must be a key to understanding unusual features of the hot QCD matter as observed at RHIC and LHC. Consequently, the confining but chirally symmetric matter above Tch can be considered as a dense system of very large and strongly overlapping meson-like states (``strings'').

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arXiv2024

Large $N_c$ QCD phase diagram at $μ_B = 0$

Lattice studies suggest that at zero baryon chemical potential and increasing temperature there are three characteristic regimes in QCD that are connected by smooth analytical crossovers: a hadron gas regime at T < T_ch ~ 155 MeV, an intermediate regime, called stringy fluid, at T_ch < T < ~ 3 T_ch, and a quark-gluon plasma regime at higher temperatures. These regimes have been interpreted to reflect different approximate symmetries and effective degrees of freedom. In the hadron gas the effective degrees of freedom are hadrons and the approximate chiral symmetry of QCD is spontaneously broken. The intermediate regime has been interpreted as lacking spontaneous chiral symmetry breaking along with the emergence of new approximate symmetry, chiral spin symmetry, that is not a symmetry of the Dirac Lagrangian, but is a symmetry of the confining part of the QCD Lagrangian. While the high temperature regime is the usual quark-gluon plasma which is often considered to reflect "deconfinement" in some way. This paper explores the behavior of these regimes of QCD as the number of colors in the theory, N_c, gets large. In the large N_c limit the theory is center-symmetric and notions of confinement and deconfinement are unambiguous. The energy density is O(N_c^0) in the meson gas, O(N_c^1) in the intermediate regime and O(N_c^2) in the quark-gluon plasma regime. In the large N_c limit these regimes may become distinct phases separated by first order phase transitions. The intermediate phase has the peculiar feature that glueballs should exist and have properties that are unchanged from what is seen in the vacuum (up to 1/N_c corrections), while the ordinary dilute gas of mesons with broken chiral symmetry disappears and approximate chiral spin symmetry should emerge.

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arXiv2024

On interpretation of fluctuations of conserved charges at high T

Fluctuations of conserved charges calculated on the lattice which can be measured experimentally, are well reproduced by a hadron resonanse gas model at temperatures below T_{ch} ~ 155 MeV and radically deviate from the hadron resonance gas predictions above the chiral restoration crossover. This behavior is typically interpreted as an indication of deconfinement in the quark-gluon plasma regime. We present an argument that this interpretation may be too simple. The argument is based on the scaling of quantities with the number of colors: demonstration of deconfinement and QGP requires observable that is sensitive to N_c^2 gluons while the conserved charges are sensitive only to quarks and above T_{ch} scale as N_c^1. The latter scaling is consistent with the existence of an intermediate regime characterized by restored chiral symmetry and by approximate chiral spin symmetry which is a symmetry of confining interaction. In this regime the energy density, pressure and entropy density scale as N_c^1. In the large N_c limit this regime might become a distinct phase separated from the hadron gas and from QGP by phase transitions. A natural observable that associates with deconfinement and is directly sensitive to deconfined N_c^2-1 gluons is the Polyakov loop; in the N_c=3 world it remains very close to 0 at temperatures well above chiral crossover, reaches the value 0.5 around 3T_{ch} and the value close to 1 at temperatures ~1 GeV.

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arXiv2024

Chiral symmetry restoration at finite temperature in a model with manifest confinement

Multiple lattice evidences support the existence of a confining but chirally symmetric regime of QCD above the chiral symmetry restoration crossover at Tch ~ 155 MeV. This regime is characterised by an approximate chiral spin symmetry of the partition function, which is a symmetry of the colour charge and the confining electric part of the QCD Lagrangian. It is traditionally believed that confinement should automatically induce spontaneous breaking of chiral symmetry, which would preclude the existence of a confining but chirally symmetric regime of QCD at high temperatures. We employ a well-known solvable quark model for QCD in 3+1 dimensions that is chirally symmetric and manifestly confining and argue that while confinement indeed induces dynamical breaking of chiral symmetry at T=0, a chiral restoration phase transition takes place at some critical temperature Tch. Above this temperature, the spectrum of the model consists of chirally symmetric hadrons with approximate chiral spin symmetry.

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arXiv2024

Chiral spin symmetry and hot QCD

In this talk we overview main results indicating existence in QCD of three qualitatively different regimes connected by smooth crossovers upon heating: a hadron gas, a stringy fluid and a quark-gluon plasma. In the combined large N_c and chiral limit these regimes likely become distinct phases separated by phase transitions: a chiral restoration phase transition around T_{ch} ~ 130 MeV and a deconfinement phase transition around T_d ~ 300 MeV. It should be an important task to verify this issue on the lattice. We will introduce a chiral spin symmetry, which is a symmetry of the electric part of electrodynamics and of QCD with light quarks. It is realized approximately in QCD above the chiral restoration crossover and disappears in the QGP regime. The center symmetry of the pure glue action and the chiral spin symmetry of the electric part of the QCD Lagrangian with light quarks are complementary to distinguish the confining regime and its disappearance. We also address other lattice evidences for stringy fluid: hadron resonances extracted from the lattice correlators; breakdown of the thermal perturbation theory at T < ~ 600 MeV and fluctuations of conserved charges that point out the N_c scaling above T ~ 155 MeV.

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arXiv2023

Chiral spin symmetry and hot/dense QCD

Above the chiral symmetry restoration crossover around T_{ch} ~ 155 MeV a new regime arises in QCD, a stringy fluid, which is characterized by an approximate chiral spin symmetry of the thermal partition function. This symmetry is not a symmetry of the Dirac Lagrangian and is a symmetry of the electric part of the QCD Lagrangian. In this regime the medium consists of the chirally symmetric and approximately chiral spin symmetric hadrons that are made of the chirally symmetric quarks connected into the color singlet compounds by a confining chromoelectric field. This regime is evidenced by the approximate chiral spin symmetry of the spatial and temporal correlators and by the breakdown of the thermal perturbation theory at the crossover between the partonic (the quark-gluon plasma) and stringy fluid regimes at ~ 3 T_{ch}. The chiral spin symmetry smoothly disappears above ~ 3T_{ch} which means that the chromoelectric confining interaction gets screened. A direct evidence that the stringy fluid medium consists of densely packed hadrons is the pion spectral function that shows a distinct pion state and its first radial excitation above T_{ch}. Another direct evidence of the hadron degrees of freedom in the stringy fluid is the bottomonium spectrum with the 1S,2S,3S and 1P,2P radial and orbital excitations that become broad with temperature. The hadrons between T_{ch} and ~ 3 T_{ch} in the stringy fluid interact strongly which makes the stringy fluid more a liquid rather than a gas. We discuss how this chiral spin symmetric regime extends into the finite chemical potentials domain and present a qualitative sketch of the QCD phase diagram.

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arXiv2021

Symmetries of temporal correlators and the nature of hot QCD

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.

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arXiv2021

A finite box as a tool to distinguish free quarks from confinement at high temperatures

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.

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arXiv2020

Three regimes of QCD

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 truncation 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.

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arXiv2020

Fluctuations of conserved charges, chiral spin symmetry and deconfinement in an SU(2)_color subgroup of SU(3)_color above T_c

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 conserved 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.

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arXiv2020

The chiral magnetic effect and the chiral spin symmetry in QCD above Tc

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.

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arXiv2020

Symmetries of the light hadron spectrum in high temperature QCD

Properties of QCD matter change significantly around the chiral crossover temperature, and the effects on $U(1)_A$ and topological susceptibilities, as well as the meson spectrum have been studied with much care. Baryons and the effect of parity doubling in this temperature range have been analyzed previously by various other groups employing different setups. Here we construct suitable operators to investigate chiral and axial $U(1)_A$ symmetries in the baryon spectrum. Measurements for different volumes and quark-masses are done with two flavors of chirally symmetric domain-wall fermions at temperatures above the critical one. The possibility of emergent $SU(4)$ and $SU(2)_{CS}$ symmetries is discussed.

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arXiv2020

Chiral-spin symmetry of the meson spectral function above $T_c$

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.

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