Chiral spin symmetry

TL;DR

The paper investigates the origin of hadron masses and the relationship between confinement and chiral symmetry breaking by introducing the chiral spin symmetry $SU(2)_{CS}$ and its flavor extensions. It presents lattice evidence from near-zero Dirac-mode truncations and finite-temperature correlators showing emergent $SU(2)_{CS}$ and $SU(4)$ symmetries, indicating that confinement is governed by the chromoelectric sector rather than solely by chiral symmetry breaking. A three-regime QCD phase diagram is proposed: hadron gas ($N_c^0$), stringy fluid ($N_c^1$), and QGP ($N_c^2$), with a distinct large-$N_c$ behavior and smooth crossovers at finite $N_c$. A manifestly confining and chirally symmetric 3+1D model illustrates chiral restoration within confinement and the delocalization and swelling of color-singlet quark–antiquark bound states, providing a microscopic picture of the stringy fluid. Overall, the work reshapes the QCD phase structure, linking lattice observations to heavy-ion phenomenology and offering a framework for understanding confinement alongside chiral dynamics across temperatures and color numbers.

Abstract

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.

Figures (10)

• Figure 1: Transformations between $J=1$ operators, $i=1,2,3$. Left panel: The left column indicates the $SU(2)_R \times SU(2)_L$ representations for every operator, with $(I_R,I_L)$ being the isospins of the right- and left-handed quarks (with the total isospin $I$ restricted to be $|I_R - I_L| \leq I \leq I_R + I_L$). $I, J^{PC}$ together with the chiral representation form a complete set of quantum numbers of the operator. Red and blue arrows connect operators which transform into each other under $SU(2)_R \times SU(2)_L$ and $U(1)_A$, respectively. $\gamma^4 = \gamma^0$. Right panel: The $J=1$$SU(2)_{CS}$ triplets (green arrows) and the $SU(4)$ 15-plet (purple). The $f_1$ operator is a singlet of $SU(4)$. Other notations are the same as in the left panel. From ref. GP.
• Figure 2: $J=1$ isovector meson masses as a function of the truncation number $k$, where $k$ represents the amount of removed lowest modes of the Dirac operator. $\sigma$ shows the energy gap in the Dirac spectrum. From ref. D1.
• Figure 3: $J=1$ isovector and isoscalar meson masses as a function of the truncation number $k$ where $k$ represents the amount of removed lowest modes of the Dirac operator. $\sigma$ shows the energy gap in the Dirac spectrum. From Ref. D2.
• Figure 4: Temporal correlation functions for $12 \times 48^3$ lattices. The l.h.s. shows correlators calculated with free noninteracting quarks with manifest $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries. The r.h.s. presents full QCD results at a temperature 220 MeV, which shows multiplets of all $U(1)_A$, $SU(2)_L \times SU(2)_R$, $SU(2)_{CS}$ and $SU(4)$ groups. From Ref. R2.
• Figure 5: Spatial correlation functions of all possible isovector $J=0,1$ bilinears. From Ref. R1.