Chiral symmetry at finite temperature: linear vs nonlinear $\sigma$-models

Abstract

The linear O($N$) sigma model undergoes a symmetry restoring phase transition at finite temperature. We show that the nonlinear O($N$) sigma model also undergoes a symmetry restoring phase transition; the critical temperatures are the same when the linear model is treated in mean field approximation and the nonlinear model is treated to leading plus subleading order in the 1/$N$ expansion. We also carefully define and study the behavior of $f_{\pi }$ and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition.

29 pages, regular Latex, 5 figures in one Postscript file

Cited by in corpus (70)

• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Droplets in the cold and dense linear sigma model with quarks
• The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation
• Chiral perturbation theory in a magnetic background - finite-temperature effects
• Linear sigma model and chiral symmetry at finite temperature
• Role of Fluctuations in the Linear Sigma Model with Quarks
• Thermal rho and sigma mesons from chiral symmetry and unitarity
• Forming Disoriented Chiral Condensates through Fluctuations
• Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories
• Vector Manifestation in Hot Matter
• Stochastic treatment of Disoriented Chiral Condensates within a Langevin description
• How pi0 -> gamma gamma changes with temperature
• Impact of a thermal medium on $D$ mesons and their chiral partners
• The Chiral Fermion Meson Model at Finite Temperature
• Vector and axialvector mesons at nonzero temperature within a gauged linear sigma model
• An Effective Lagrangian with Broken Scale and Chiral Symmetry III: Mesons at Finite Temperature
• Selfconsistent calculations of spectral densities in the O(N) model: improving the Hartree-Fock approximation by including nonzero decay widths
• Thermodynamics of O(N) sigma models: 1/N corrections
• Vector Manifestation and Violation of Vector Dominance in Hot Matter
• The Fading of Symmetry Non-restoration at Finite Temperature
• Modelling the QCD Phase Transition with an Effective Lagrangian of Light and Massive Hadrons
• The Pion Decay Constants and the Rho-Meson Mass at Finite Temperature in the Hidden Local Symmetry
• The thermal coupling constant and the gap equation in the $\lambda {\varphi }_D^4$ model
• Scattering of soft, cool pions
• Thermal Dilepton Production from Dropping rho based on the Vector Manifestation
• An Effective Lagrangian with Broken Scale and Chiral Symmetry IV: Nucleons and Mesons at Finite Temperature
• The role of the thermal $f_0(500)$ in chiral symmetry restoration
• Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Pion Decay Constant at Finite Temperature in the Nonlinear Sigma Model
• Restoration of chiral symmetry in the large-N_c limit
• Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method
• Thermodynamics of the O(N) Nonlinear Sigma Model in 1+1 Dimensions
• Massive Yang-Mills for Vector and Axial-Vector Spectral Functions at Finite Temperature
• Possible Pseudogap Phase in QCD
• Dissipation at Two-Loop Level: Undressing the Chiral Condensate
• Skyrmions at finite density and temperature: the chiral phase transition
• The O(2) model in polar coordinates at nonzero temperature
• Dynamical Evolution of the Scalar Condensate in Heavy Ion Collisions
• Consequences of the partial restoration of chiral symmetry in AdS/QCD
• Large-$N$ pion scattering at finite temperature: the $f_0(500)$ and chiral restoration
• Effects from inhomogeneities in the chiral transition
• Hard Thermal Loops and Chiral Lagrangians
• Chiral Symmetry Restoration for the large-$N$ pion gas
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Degeneracy patterns of chiral companions at finite temperature
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• Ambiguities in the zero momentum limit of the thermal ${\pi }^o\gamma \gamma$ triangle diagram
• The Electromagnetic Mass Difference of Pions at Low Temperature
• Light quarks at finite temperature: chiral restoration and the fate of the $U(1{)}_A$ symmetry
• Chiral Phase Transition and Baryon Number Conservation
• One-loop dimensional reduction of the linear sigma model
• On the Thermal Gauge Boson Masses of the Electroweak Theory in the Broken Phase
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal $\sigma$ pole trajectory with cross-channel improvements
• Hot Nucleons in Chiral Soliton Models
• Chiral Phase Transition in QCD and Vector Manifestation
• Chiral symmetry breaking and pion condensation in the early universe
• Anomalous processes at high temperature and density in a 2-dimensional linear $\sigma$ model
• Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory
• Dimensional reduction of the chiral-continous Gross-Neveu model
• Pion Mass Shift and the Kinetic Freeze Out Process
• The speed of cool soft pions
• Nonequilibrium chiral perturbation theory and pion decay functions
• Chiral Estimate of QCD Pseudocritical Line
• Disoriented chiral condensate in presence of dissipation and noise
• Pion production in nonequilibrium Chiral perturbation Theory
• Transport coefficients of chiral fluid dynamics using low-energy effective models
• Finite Temperature Effects and Axion Cosmology
• Initial State of Disoriented Chiral Condensate Formation