Renormalization Group Approach towards the QCD Phase Diagram

Abstract

The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are then applied to the strong interaction in the framework of an effective quark meson model which is introduced in great detail. The renormalization group analysis of the two flavor quark meson model is extended to finite temperature and quark chemical potential which allows for an analysis of the chiral phase diagram beyond the mean field approximation.

14 pages, no figures; Lecture held by the first author at the 2006 Helmholtz International Summer School "Dense Matter in Heavy-Ion Collisions and Astrophysics", JINR, Dubna, Russia

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Cited by in corpus (114)

• The nonperturbative functional renormalization group and its applications
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• Quark Confinement from Color Confinement
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Chiral symmetry breaking in continuum QCD
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Inhomogeneous chiral condensates
• Landau gauge Yang-Mills correlation functions
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Global Flows in Quantum Gravity
• Confinement from Correlation Functions
• On the phase structure and thermodynamics of QCD
• Quark-meson-diquark model for two-color QCD
• Improved Polyakov-loop potential for effective models from functional calculations
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
• Thermodynamics of QCD at vanishing density
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Higher order quark-mesonic scattering processes and the phase structure of QCD
• The Vacuum Structure of Vector Mesons in QCD
• Hyper-order baryon number fluctuations at finite temperature and density
• Numerical analytic continuation of Euclidean data
• QCD at finite temperature and density within the fRG approach: An overview
• On the Phase Structure of QCD in a Finite Volume
• Fluctuation-induced modifications of the phase structure in (2+1)-flavor QCD
• In-Medium Spectral Functions of Vector- and Axial-Vector Mesons from the Functional Renormalization Group
• Fluctuations and the axial anomaly with three quark flavors
• Non-perturbative finite-temperature Yang-Mills theory
• FormTracer - A Mathematica Tracing Package Using FORM
• On the relevance of matter and glue dynamics for baryon number fluctuations
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Ultracold atoms and the Functional Renormalization Group
• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Hybrid and quark star matter based on a non-perturbative equation of state
• Ising and Gross-Neveu model in next-to-leading order
• Functional renormalization group studies of nuclear and neutron matter
• Universal Aspects of QCD-like Theories
• Analytic continuation of functional renormalization group equations
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Polyakov-Quark-Meson-Diquark Model for two-color QCD
• Correlation functions of three-dimensional Yang-Mills theory from the FRG
• Phase diagram of two-color quark matter at nonzero baryon and isospin density
• Finite temperature spectral functions in the O(N)-model
• Flow equations for spectral functions at finite external momenta
• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
• Fluctuations and isentropes near the chiral critical endpoint
• Non-equilibrium phase transition in relativistic nuclear collisions: Importance of the equation of state
• Mass sensitivity of the three-flavor chiral phase transition
• Chiral Mirror-Baryon-Meson Model and Nuclear Matter beyond Mean-Field
• Efimov effect from functional renormalization
• Nonperturbative quark matter equations of state with vector interactions
• The application of the Quark-Hadron Chiral Parity-Doublet Model to neutron star matter
• Deep learning stochastic processes with QCD phase transition
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• Phase structure of spin-imbalanced unitary Fermi gases
• Pseudo-fermion functional renormalization group for spin models
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Functional Renormalization Group Study of the Chiral Phase Transition Including Vector and Axial-vector Mesons
• On the efficient computation of high-order derivatives for implicitly defined functions
• Bound state properties from the Functional Renormalisation Group
• Functional renormalization group study of the Quark-Meson model with $\omega$ meson
• DoFun 3.0: Functional equations in Mathematica
• Shocks and quark-meson scatterings at large density
• Vector and Axial-Vector Mesons in Nuclear Matter
• Critical temperature and superfluid gap of the Unitary Fermi Gas from Functional Renormalization
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Strangeness Neutrality and QCD Thermodynamics
• Dimensional crossover of nonrelativistic bosons
• Fermionic spectral functions with the Functional Renormalization Group
• Functional renormalization group at finite density and Bose condensation
• Dense two-color QCD from Dyson-Schwinger equations
• Low-energy limit of the $O(4)$ quark-meson model from the functional renormalization group approach
• On critical scaling at the QCD N_f=2 chiral phase transition
• Strangeness neutrality and baryon-strangeness correlations
• Real-time methods for spectral functions
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Scaling relations and multicritical phenomena from Functional Renormalization
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover
• Mesonic dynamics and QCD phase transition
• Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover
• Dynamical generation of low-energy couplings from quark-meson fluctuations
• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• Sarma phase in relativistic and non-relativistic systems
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• Baryon number probability distribution at finite temperature
• Spectral functions and in-medium properties of hadrons
• Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges
• Fermionic excitations at finite temperature and density
• Regulator scheme dependence of the chiral phase transition at high densities
• Spectral Functions from the Functional Renormalization Group
• Efimov physics from the functional renormalization group
• Correlations of conserved charges and QCD phase structure
• Error estimates and specification parameters for functional renormalization
• Spectral functions from the functional renormalization group at finite temperature and density
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Consistent approach to study gluon quasi-particles
• Real-time observables from Euclidean thermal correlation functions
• A comprehensive approach to the physics of mesons
• Center phase transition from matter propagators in (scalar) QCD
• Few-body hierarchy in non-relativistic functional renormalization group equations and a decoupling theorem
• Effect of momentum anisotropy on quark matter in the quark-meson model
• Nonuniform-temperature effects on the phase transition in an Ising-like model
• Phase Structure and Dynamics of QCD-- A Functional Perspective
• Spontaneously broken ground states of the U(n)_L x U(n)_R linear sigma model at large n
• Partial wave analysis for the in-hadron condensate
• Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators
• QCD Green's Functions and Phases of Strongly-Interacting Matter
• Pion superfluid phase transition at finite isospin chemical potential
• An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers
• Functional Renormalization Analytically Continued
• Critical structure of the QCD medium