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Register a new userGluon Condensate at finite temperature and density in holographic QCD
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Floriana Giannuzzi
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The lowest dimensional gluon condensate $G_2$ is analysed at finite temperature and chemical potential using a bottom/up holographic model of QCD. Starting from the free energy of the model, pressure, entropy and quark density are obtained. Moreover, at zero chemical potential, the temporal and spatial Wilson loops at low temperature are computed; they are related to the (chromo-)electric and magnetic components of $G_2$, respectively.
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We investigate the quark-gluon mixed condensate based on an AdS/QCD model. Introducing a holographic field dual to the operator for the quark-gluon mixed condensate, we obtain the corresponding classical equation of motion. Taking the mixed condensate as an additional free parameter, we show that the present scheme reproduces very well experimental data. A fixed value of the mixed condensate is in good agreement with that of the QCD sum rules.
We discuss the phase structure of QCD for $N_f=2$ and $N_f=2+1$ dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for $mu_B/T lesssim 6$. We find a critical endpoint at $(T_text{CEP},{mu_B}_{text{CEP}})=(107, 635),text{MeV}$. The curvature of the phase boundary at small chemical potential is $kappa=0.0142(2)$, computed from the renormalised light chiral condensate $Delta_{l,R}$. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for $mu_Bgtrsim 417$ MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.
In this paper we study the dynamical instability of Sakai-Sugimotos holographic QCD model at finite baryon density. In this model, the baryon density, represented by the smeared instanton on the worldvolume of the probe D8-overline{D8} mesonic brane, sources the worldvolume electric field, and through the Chern-Simons term it will induces the instability to form a chiral helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form the chiral density wave for large N_c QCD at finite density. Our results show that this kind of instability occurs for sufficiently high baryon number densities. The phase diagram of holographic QCD will thus be changed from the one which is based only on thermodynamics. This holographic approach provides an effective way to study the phases of QCD at finite density, where the conventional perturbative QCD and lattice simulation fail.
The lowest dimensional gluon condensate $G_2$ is analyzed at finite temperature and chemical potential using a holographic model of QCD with conformal invariance broken by a background dilaton. Starting from the free energy of the model, the thermodynamical quantities needed to determine the $T$ and $mu$ dependence of the gluon condensate are evaluated. At high temperature the gluon condensate is independent of chemical potential. Moreover, at $mu=0$ and in the string frame, the temporal and spatial Wilson loops at low temperature are computed; they are related to the (chromo) electric and magnetic components of $G_2$, respectively. The $T$-dependence of the two components is separately determined.
It is shown that the spin polarized condensate appears in quark matter at high baryon density and low temperature due to the tensor-type four-point interaction in the Nambu-Jona-Lasinio-type model as a low energy effective theory of quantum chromodynamics. It is indicated within this low energy effective model that the chiral symmetry is broken again by the spin polarized condensate as increasing the quark number density, while the chiral symmetry restoration occurs in which the chiral condensate disappears at a certain density.
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