Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Tan, Yang-yang; Chen, Yongrui; Fu, Weijie

doi:10.21468/scipostphys.12.1.026

Cited by 10 publications

(14 citation statements)

References 77 publications

(129 reference statements)

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“…One can see that when temperature is large, one has a negative spectral function in the regime of small p 0 , and there is a minus peak structure around the pole mass. It is found that the negative spectral function results from the contributions of the Landau damping, and see [277] for a more detailed discussion. Nonetheless, when the temperature is decreased below about 60 MeV, the Landau damping is dominated by the process of creation and annihilation of particles, and the spectral function is positive.…”

Section: Spectral Functions and Dynamical Critical Exponentmentioning

confidence: 97%

“…In this section we would like to discuss the fRG formulated on the Keldysh path at the example of the O(N ) scalar theory [277].…”

Section: Real-time Frgmentioning

confidence: 99%

“…A line with an empty circle inserted in the middle is used to denote the Keldysh propagator, which results from Equation (280). The plot is adopted from [277].…”

Section: A Frg With the Keldysh Functional Integralmentioning

confidence: 99%

“…Diagrammatic representation of the flow equation of the four-point vertex in the symmetric phase. The plot is adopted from [277].…”

Section: A Frg With the Keldysh Functional Integralmentioning

confidence: 99%

“…Note that the wave function renormalization Z φ,k = 1 is adopted to simplify the calculation of ∂τ I k (p) in Equation (295). The explicit expression of I k (p) can be found in [277].…”

Section: Flows Of the Two-and Four-point Correlation Functionsmentioning

confidence: 99%

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QCD at finite temperature and density within the fRG approach: An overview

2022

Preprint

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In this paper we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated in successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc., are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson-Schwinger Equations, which passes through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with µB 420 MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments, could arise from the increasingly sharp crossover in the regime of low collision energy.

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Section: Spectral Functions and Dynamical Critical Exponentmentioning

confidence: 97%

“…In this section we would like to discuss the fRG formulated on the Keldysh path at the example of the O(N ) scalar theory [277].…”

Section: Real-time Frgmentioning

confidence: 99%

“…A line with an empty circle inserted in the middle is used to denote the Keldysh propagator, which results from Equation (280). The plot is adopted from [277].…”

Section: A Frg With the Keldysh Functional Integralmentioning

confidence: 99%

“…Diagrammatic representation of the flow equation of the four-point vertex in the symmetric phase. The plot is adopted from [277].…”

Section: A Frg With the Keldysh Functional Integralmentioning

confidence: 99%

“…Note that the wave function renormalization Z φ,k = 1 is adopted to simplify the calculation of ∂τ I k (p) in Equation (295). The explicit expression of I k (p) can be found in [277].…”

Section: Flows Of the Two-and Four-point Correlation Functionsmentioning

confidence: 99%

See 3 more Smart Citations

QCD at finite temperature and density within the fRG approach: An overview

2022

Preprint

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Critical dynamics in a real-time formulation of the functional renormalization group

Roth,

von Smekal

2023

J. High Energ. Phys.

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We present first calculations of critical spectral functions of the relaxational Models A, B, and C in the Halperin-Hohenberg classification using a real-time formulation of the functional renormalization group (FRG). We revisit the prediction by Son and Stephanov that the linear coupling of a conserved density to the non-conserved order parameter of Model A gives rise to critical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistent expansion schemes in the 1PI vertex functions as truncations of the effective average action suitable for real-time applications, and analyze in detail how the different critical dynamics are properly incorporated in the framework of the FRG on the closed-time path. We present results for the corresponding critical spectral functions, extract the dynamic critical exponents for Models A, B, and C, in two and three spatial dimensions, respectively, and compare the resulting values with recent results from the literature.

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QCD at finite temperature and density within the fRG approach: an overview

Fu¹

2022

Commun. Theor. Phys.

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In this paper we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated in successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc., are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson-Schwinger Equations, which passes through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with $\mu_B\gtrsim 420$ MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments, could arise from the increasingly sharp crossover in the regime of low collision energy.

show abstract

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Cited by 10 publications

References 77 publications

QCD at finite temperature and density within the fRG approach: An overview

QCD at finite temperature and density within the fRG approach: An overview

Critical dynamics in a real-time formulation of the functional renormalization group

QCD at finite temperature and density within the fRG approach: an overview

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