The Roberge-Weiss transition and 't Hooft loops

Abstract

Roberge and Weiss showed that for SU(N) gauge theories, phase transitions occur in the presence of an imaginary quark chemical potential. We show that at asymptotically high temperature, where the phase transition is of first order, that even with dynamical quarks 't Hooft loops of arbitrary Z(N) charge are well defined at the phase boundary. To leading order in weak coupling, the 't Hooft loop satisfies Casimir scaling in the pure glue theory, but not with quarks. Because the chemical potential is imaginary, typically the interaction measure is negative on one side of the phase transition. Using a matrix model to model the deconfining phase transition, we compute the phase diagram for heavy quarks, in the plane of temperature and imaginary chemical potential. In general we find intersecting lines of first order transitions. Using a modified Polyakov loop which is Roberge-Weiss symmetric, we suggest that the interface tension is related to the 't Hooft loop only at high temperature, where the imaginary part of this Polyakov loop, and not the real part, is discontinuous across the phase boundary.

30 pages, 8 figures, 1 table. Expanded version: clarified relationship of interface tension to 't Hooft loop; phase diagram for heavy quarks computed; numerous references added

References in corpus (16)

• 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
• Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential
• Effective matrix model for deconfinement in pure gauge theories
• How Wide is the Transition to Deconfinement?
• Phase diagram in the imaginary chemical potential region and extended Z3 symmetry
• Determination of QCD phase diagram from the imaginary chemical potential region
• The Roberge-Weiss endpoint in N_f = 2 QCD
• Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions
• Critical endpoint for deconfinement in matrix and other effective models
• Vector-type four-quark interaction and its impact on QCD phase structure
• Quasiparticle Model of Quark-Gluon Plasma at Imaginary Chemical Potential
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• Violations of parity and charge conjugation in the theta vacuum with imaginary chemical potential
• Two-color QCD at imaginary chemical potential and its impact on real chemical potential
• Investigation of meson masses for real and imaginary chemical potential

Cited by in corpus (17)

• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• Production and Elliptic Flow of Dileptons and Photons in the semi-Quark Gluon Plasma
• Roberge-Weiss endpoint at the physical point of $N_f=2+1$ QCD
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Anomaly matching in QCD thermal phase transition
• Universal aspects of the phase diagram of QCD with heavy quarks
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Roberge-Weiss endpoint and chiral symmetry restoration in $N_f=2+1$ QCD
• Quark number holonomy and confinement-deconfinement transition
• Free energy of a Holonomous Plasma
• Gauge-invariant screening masses and static quark free energies in $N_f=2+1$ QCD at non-zero baryon density
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• Deconfinement in the presence of a strong magnetic field
• Wilson loops in the Hamiltonian formalism
• Shear and bulk viscosity for a pure glue theory using an effective matrix model