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Register a new userChiral and effective $U(1)_{rm A}$ symmetry restoration in QCD
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The nature and location of the QCD phase transition close to the chiral limit restricts the phase structure of QCD with physical pion masses at non-vanishing density. At small pion masses, explicit $U(1)_{rm A}$-breaking, as induced by a non-trivial topological density, is of eminent importance. It triggers the t Hooft interactions and also manifests itself in the interplay of four-quark interactions at low momentum scales. In the present work, we perform a Fierz-complete analysis of the emergence of four-quark interactions from the QCD dynamics at finite temperature, subject to a given t Hooft coupling at large momentum scales. The variation of the latter allows us to test the robustness of our findings. Taking an estimate of the effect of the topological running of the t Hooft coupling into account, our analysis suggests that the chiral transition in QCD with two massless quark flavours falls into the $O(4)$ universality class.
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We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_tau = 8 and spatial extent N_sigma = 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_pi = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.
We consider the noncommutative deformation of the Sakai--Sugimoto model at finite temperature and finite baryon chemical potential. The space noncommutativity is possible to have an influence on the flavor dynamics of the QCD. The critical temperature and critical value of the chemical potential are modified by the space noncommutativity. The influence of the space noncommutativity on the flavor dynamics of the QCD is caused by the Wess--Zumino term in the effective action of the D8-branes. The intermediate temperature phase, in which the gluons deconfine but the chiral symmetry remains broken, is easy to be realized in some region of the noncommutativity parameter.
We incorporate the effective restoration of $U(1)_{rm A}$ symmetry in the 2+1 flavor entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model by introducing a temperature-dependent strength $K(T)$ to the Kobayashi-Maskawa-t Hooft (KMT) determinant interaction. $T$ dependence of $K(T)$ is well determined from pion and $a_0$-meson screening masses obtained by lattice QCD (LQCD) simulations with improved p4 staggered fermions. The strength is strongly suppressed in the vicinity of the pseudocritical temperature of chiral transition. The EPNJL model with the $K(T)$ well reproduces meson susceptibilities calculated by LQCD with domain-wall fermions. The model shows that the chiral transition is second order at the light-quark chiral-limit point where the light quark mass is zero and the strange quark mass is fixed at the physical value. This indicates that there exists a tricritical point. Hence the location is estimated.
We discuss the phases of QCD in the parameter space spanned by the number of light flavours and the temperature with respect to the realisation of chiral and conformal symmetries. The intriguing interplay of these symmetries is best studied by means of lattice simulations, and some selected results from our recent work are presented here.
Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c approx 8 pm 1$, in agreement with the state-of-the-art direct lattice analysis of chiral symmetry restoration in QCD.
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