Anomaly matching in QCD thermal phase transition

Abstract

We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a ${\mathbb{Z}}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the ${\mathbb{Z}}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly before and after QCD phase transition. The effect of the imaginary chemical potential is suppresssed in the large $N$ expansion, and we discuss implications of the 't~Hooft anomaly matching for the nature of QCD phase transition with and without the imaginary chemical potential. Arguments based on universality alone are disfavored, and a first order phase transition may be the simplest possibility if the large $N$ expansion is qualitatively good.

41 pages, 5 figures. V2: references added

References in corpus (31)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• A holographic model of deconfinement and chiral symmetry restoration
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Analytic continuation of the critical line: suggestions for QCD
• On the critical line of 2+1 flavor QCD
• Determination of QCD phase diagram from the imaginary chemical potential region
• The Roberge-Weiss endpoint in N_f = 2 QCD
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Dai-Freed theorem and topological phases of matter
• Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions
• Order parameters and color-flavor center symmetry in QCD
• Curvature of the chiral pseudo-critical line in QCD
• How to get from imaginary to real chemical potential
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• The critical line from imaginary to real baryonic chemical potentials in two-color QCD
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Imaginary chemical potentials and the phase of the fermionic determinant
• Quark number densities at imaginary chemical potential in $N_f=2$ lattice QCD with Wilson fermions and its model analyses
• Notes on natural inflation
• 't Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate
• Nature of Roberge-Weiss transition end points for heavy quarks in $N_f=2$ lattice QCD with Wilson fermions
• Two-color QCD at imaginary chemical potential and its impact on real chemical potential

Cited by in corpus (6)

• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• High-temperature domain walls of QCD with imaginary chemical potentials
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly