[Paper Review] SU(2N_F) symmetry of QCD at high temperature and its implications

L. Ya. Glozman|arXiv (Cornell University)|Oct 2, 2016

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper proposes that at high temperatures, QCD exhibits an unbroken SU(2N_F) symmetry—beyond the standard chiral and U(1)_A symmetries—due to the restoration of both chiral and axial U(1) symmetries. This symmetry forbids deconfined quarks and gluons, implying that QCD remains in a confining phase above T_c, with only SU(2N_F)-symmetric composite ''hadrons'' as physical degrees of freedom.

ABSTRACT

If above a critical temperature not only the SU(N_F)_L imes SU(N_F)_R chiral symmetry of QCD but also the U(1)_A symmetry is restored, then the actual symmetry of the QCD correlation functions and observables is SU(2N_F). Such a symmetry prohibits existence of deconfined quarks and gluons. Hence QCD at high temperature is also in the confining regime and elementary objects are SU(2N_F) symmetric "hadrons" with not yet known properties.

Motivation & Objective

• To investigate whether the restoration of both chiral and U(1)_A symmetries at high temperature leads to a larger global symmetry in QCD.
• To challenge the conventional view that QCD deconfines above T_c by showing that SU(2N_F) symmetry forbids free quarks and gluons.
• To identify the role of near-zero Dirac eigenmodes in generating the SU(2N_F) symmetry and its breaking via anomalies.
• To propose that physical degrees of freedom above T_c are not free quarks but SU(2N_F)-symmetric ''hadrons'' with unknown properties.
• To provide testable lattice-QCD predictions for SU(2N_F) and SU(2)_CS symmetry restoration in meson and baryon correlation functions.

Proposed method

• Analyzes the QCD partition function in Euclidean space, focusing on the Dirac operator's eigenmodes and their transformation properties under SU(2)_CS and SU(2N_F) groups.
• Uses the Banks-Casher relation to link the quark condensate to the density of near-zero Dirac eigenmodes.
• Demonstrates that the partition function is invariant under local SU(2)_CS and SU(2N_F) transformations when exact zero modes (which break the symmetry) are excluded in the thermodynamic limit.
• Identifies the axial U(1)_A anomaly as the mechanism that breaks SU(2)_CS and SU(2N_F), while the condensation of low-lying Dirac modes at m→0 breaks the symmetry spontaneously.
• Constructs hadronic operators transforming under SU(2)_CS and SU(2N_F) and derives their correlation function behavior under symmetry restoration.
• Proposes lattice tests based on degeneracy of meson and baryon correlators above T_c, with vanishing off-diagonal components for SU(2)_CS multiplets.

Experimental results

Research questions

• RQ1 Does the simultaneous restoration of chiral SU(N_F)_L × SU(N_F)_R and U(1)_A symmetry in QCD at high temperature lead to an enhanced SU(2N_F) global symmetry?
• RQ2 Can the SU(2N_F) symmetry be realized as a hidden classical symmetry in the nonperturbative Euclidean formulation of QCD?
• RQ3 Why do lattice simulations with overlap fermions show degeneracy of chiral and U(1)_A-related states beyond the chiral multiplet structure?
• RQ4 Does the SU(2N_F) symmetry forbid the existence of deconfined quarks and gluons in the high-temperature phase of QCD?
• RQ5 What are the observable signatures of SU(2N_F) symmetry restoration in correlation functions of mesons and baryons on the lattice?

Key findings

• The SU(2N_F) symmetry emerges as a hidden classical symmetry in the nonperturbative Euclidean formulation of QCD when exact zero modes are excluded in the thermodynamic limit.
• The SU(2N_F) symmetry is broken both by the axial anomaly and by the quark condensate, but is restored at high temperature when both chiral and U(1)_A symmetries are restored.
• Deconfined quarks and gluons cannot exist in the high-temperature phase of QCD because their Green functions are not SU(2N_F)-symmetric due to chromo-magnetic interactions.
• Physical degrees of freedom above T_c are not free quarks but color-singlet, SU(2N_F)-symmetric ''hadrons'' whose properties remain unknown.
• Lattice tests predict that above T_c, diagonal correlation functions of SU(2)_CS multiplets (e.g., 1^{--} mesons) become degenerate and off-diagonal correlators vanish.
• The observed degeneracy in lattice simulations of N_F=2 QCD beyond chiral multiplets is explained by the SU(2N_F) symmetry, not by the standard chiral Lagrangian.