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Register a new userChiral Symmetry of SYM theory in hyperbolic space at finite temperature
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We study a holographic gauge theory living in the AdS$_4$ space-time at finite temperature. The gravity dual is obtained as a solution of the type IIB superstring theory with two free parameters, which correspond to four dimensional (4D) cosmological constant ($lambda$) and the dark radiation ($C$) respectively. The theory studied here is in confining and chiral symmetry broken phase for $lambda <0$ and small $C$. When $C$ is increased, the transition to the deconfinement phase has been observed at a finite value of $C/|lambda|$. It is shown here that the chiral symmetry is still broken for a finite range of $C/|lambda|$ in the deconfinement phase. In other words, the chiral phase transition occurs at a larger value of $C/|lambda|$ than the one of the deconfinement transition. So there is a parameter range of a new deconfinement phase with broken chiral symmetry. In order to study the properties of this phase, we performed a holographic analysis for the meson mass-spectrum and other quantities in terms of the probe D7 brane. The results of this analysis are compared with a linear sigma model. Furthermore, the entanglement entropy is examined to search for a sign of the chiral phase trantion. Several comments are given for these analyses.
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Modifications of baryon properties due to the restoration of the chiral symmetry in an external hot and dense baryon medium are investigated in an effective chiral quark-meson theory. The nucleon arises as a soliton of the Gell-Mann - Levi $zs$-model, the parameters of which are chosen to be the medium-modified meson values evaluated within the Nambu - Jona-Lasinio model. The nucleon properties are obtained by means of variational projection techniques. The nucleon form factors as well as the nucleon delta transition form factors are evaluated for various densities and temperatures of the medium. Similar to the chiral phase transition line the critical curve in the $T-zr$ plane for delocalization of the nucleon is non-monotonic and this feature is reflected in all nucleon properties. At medium densities of about $(2-3) rnm$ the baryonic phase exists only at intermediate temperatures. For finite temperature and densities the nucleon form factors get strongly reduced at finite transfer momenta.
We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an $SU(2)$ doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global $SU(2)$ transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.
We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the $SU(N_c)$ SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for ${cal N}=2$ SYM theory and the analysis is extended to the finite temperature deconfinement and the zero temperature confinement phases of the Yang-Mills (YM) theory. By comparing the obtained production rates with the one of the supersymmetric case, the dynamical quark mass is estimated and we find how it varies with the chiral condensate. Based on this analysis, we give a speculation on the extension of the Nambu-Jona-Lasinio model to the finite temperature YM theory, and four fermi coupling is evaluated in the confinement theory.
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