Euclidean solutions and finite temperature gauge theory

2015

Mod. Phys. Lett. A

We investigate the thermal conductivity (κ) of the quark matter at finite quark chemical potential (µ) and temperature (T ), employing the Green-Kubo formula, for the SU(2) light-flavor sector with the finite current-quark mass m = 5 MeV. As a theoretical framework, we construct an effective thermodynamic potential from the (µ, T )-modified liquid-instanton model (mLIM). Note that all the relevant model parameters are designated as functions of T , using the trivial-holonomy caloron solution. By solving the self-consistent equation of mLIM, we acquire the constituent-quark mass M0 as a function of T and µ, satisfying the universal-class patterns of the chiral phase transition. From the numerical results for κ, we observe that there emerges a peak at µ ≈ 200 MeV for the low-T region, i.e. T 100 MeV. As T increase over T ≈ 100 MeV, the curve for κ is almost saturated as a function of T in the order of ∼ 10 −1 GeV 2 , and grows with respect to µ smoothly. At the normal nuclear-matter density ρ0 = 0.17 fm −3 , κ shows its maximum 6.22 GeV 2 at T ≈ 10 MeV, then decreases exponentially down to κ ≈ 0.2 GeV 2 . We also compute the ratio of κ and the entropy density, i.e. κ/s as a function of (µ, T ) which is a monotonically decreasing function for a wide range of T , then approaches a lower bound at very high T : κ/smin 0.3 GeV −1 in the vicinity of µ = 0.

Section: B Instantons At Finite Temperature: Caloron Solutionmentioning

confidence: 99%

Thermal conductivity of the quark matter for the SU(2) light-flavor sector

2015

Mod. Phys. Lett. A

“…Harrington-Shepard caloron [13,14]. Firstly, we want to explain briefly how to modifyρ andR as functions of T , using the caloron solution.…”

Section: Temperature-dependent Model Parametersmentioning

confidence: 99%

“…To extend LIM to a finite-T system, the model parameters of LIM, i.e. the average (anti)instanton size (ρ) and inter-(anti)instanton distanceR, are modified as functions of T using the trivial-holonomy caloron solution [13][14][15]. Note that these modifications result in the partial chiral restoration of the parameters.…”

Section: Introductionmentioning

confidence: 99%

Quark–gluon mixed condensate for the SU(2) light-flavor sector at finite temperature

2013

Physics Letters B

We investigate the quark-gluon mixed condensate qσ · Gq ≡ m 2 0 qq for the SU(2) light-flavor sector at finite temperature (T ). Relevant model parameters, such as the average (anti)instanton size, inter-(anti)instanton distance, and constituent-quark mass at zero virtuality, are modified as functions of T , employing the trivial-holonomy caloron solution. By doing that, we observe correct chiral restoration patterns depending on the current-quark mass m. We also perform the two-loop renormalization-group (RG) evolution for the both condensates by increasing the renormalization scale µ = (0.6 → 2.0) GeV. It turns out that the mixed condensate is insensitive to the RG evolution, whereas the quark condensate become larger considerably by the evolution. Numerically, we obtain − qσ ·Gq 1/5 = (0.45 ∼ 0.46) GeV at T = 0 within the present theoretical framework, and the mixed condensate plays the role of the chiral order parameter for finite T . The ratio of the two condensates m 2 0 is almost flat below the chiral transition T (T0), and increases rapidly beyond it. From a simple linear parametrization, we obtain m 2 0 (T )/m 2 0 (0) ≈ (0.07, 0.47) T /T0 + (1, 0.6) for (T T0, T T0) at µ = 0.6 GeV. The present results are compared with other theoretical ones including the lattice QCD simulations, and show qualitatively good agreement with them.

“…However, more realistic situation near T c is quite complicated as indicated in Refs. [31,37], in which the temporally periodic instantons with the trivial holonomy, i.e., the Harrington-Shepard caloron was employed [30]. These works showed that the relevant quantities decrease with respect to T smoothly, and they beomce finite even beyond T c .…”

Section: Instanton At Zero Temperature (T = 0)mentioning

confidence: 99%

An effective thermodynamic potential from the instanton with Polyakov-loop contributions

J. Phys. G: Nucl. Part. Phys.

2010

We derive an effective thermodynamic potential (Ω eff ) at finite temperature (T = 0) and zero quark-chemical potential (µR = 0), using the singular-gauge instanton solution and Matsubara formula for Nc = 3 and N f = 2 in the chiral limit. The momentum-dependent constituent-quark mass is also obtained as a function of T , employing the Harrington-Shepard caloron solution in the large-Nc limit. In addition, we take into account the imaginary quark-chemical potential µI ≡ A4, translated as the traced Polayakov-loop (Φ) as an order parameter for the Z(Nc) symmsetry, characterizing the confinement (intact) and deconfinement (spontaneously broken) phases. As a result, we observe the crossover of the chiral (χ) order parameter σ 2 and Φ. It also turns out that the critical temperature for the deconfinment phase transition, T