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Confinement versus Chiral Symmetry

Agnes Mocsy, Francesco Sannino, Kimmo Tuominen

TL;DR

The paper investigates why confinement and chiral symmetry restoration are linked in gauge theories with fundamental quarks and how this relation changes for adjoint quarks. It introduces an effective Lagrangian with a chiral order parameter and a Polyakov-loop field, coupled by symmetry-allowed interactions, to study the transfer of critical behavior to non-critical fields. For fundamental quarks, chiral restoration drives deconfinement via infrared-sensitive shifts in the Polyakov-loop sector; for adjoint quarks, the two transitions can be entangled even without a cubic coupling, leaving distinct but connected signatures in screening masses and correlators. The approach provides a framework to interpret lattice results and extend to finite density, offering insights into a broad class of phase transitions in QCD-like theories.

Abstract

We construct an effective Lagrangian which illustrates why color deconfines when chiral symmetry is restored in hot gauge theories with quarks in the fundamental representation. For quarks in the adjoint representation we show that while deconfinement and the chiral transition do not need to coincide, entanglement between them is still present. Extension to the chemical potential driven transition is discussed.

Confinement versus Chiral Symmetry

TL;DR

The paper investigates why confinement and chiral symmetry restoration are linked in gauge theories with fundamental quarks and how this relation changes for adjoint quarks. It introduces an effective Lagrangian with a chiral order parameter and a Polyakov-loop field, coupled by symmetry-allowed interactions, to study the transfer of critical behavior to non-critical fields. For fundamental quarks, chiral restoration drives deconfinement via infrared-sensitive shifts in the Polyakov-loop sector; for adjoint quarks, the two transitions can be entangled even without a cubic coupling, leaving distinct but connected signatures in screening masses and correlators. The approach provides a framework to interpret lattice results and extend to finite density, offering insights into a broad class of phase transitions in QCD-like theories.

Abstract

We construct an effective Lagrangian which illustrates why color deconfines when chiral symmetry is restored in hot gauge theories with quarks in the fundamental representation. For quarks in the adjoint representation we show that while deconfinement and the chiral transition do not need to coincide, entanglement between them is still present. Extension to the chemical potential driven transition is discussed.

Paper Structure

This paper contains 3 sections, 12 equations, 1 figure.

Table of Contents

  1. Fundamental Representation
  2. Adjoint Representation
  3. Discussion

Figures (1)

  • Figure 1: Left panel: Behavior of the expectation values of the Polyakov loop and chiral condensate close to the chiral phase transition as a function of the temperature, with quarks in the fundamental representation. Right panel: Same as in left panel, for quarks in the adjoint representation and $T_{\rm{c}\chi}\ll T_{\rm{c}\sigma}$ (see discussion in the text).