Abstract
Finite isospin chemical potential μI and temperature T have been introduced in the framework of soft-wall AdS/QCD model. By self-consistently solving the equation of motion, we obtain the phase boundary of pion condensation phase, across which the system undergoes a phase transition between pion condensation phase and normal phase. Compar- ing the free energy of solutions with and without pion condensation, we find that the phase transition is of first order type both at large μI and small μI. Qualitatively, the behavior at large μI is in agreement with the lattice simulation in [6], while the behavior at small μI is different from lattice simulations and previous studies in hard wall AdS/QCD model. This indicates that a full back-reaction model including the interaction of gluo-dynamics and chiral dynamics might be necessary to describe the small μI pion condensation phase. This study could provide certain clues to build a more realistic holographic model.
Highlights
The growth will ceased at ceratin μI and pion condensation starts to decrease to zero [6] at large μI (see figure 1(b), taken from [6])
Comparing the free energy of solutions with and without pion condensation, we find that the phase transition is of first order type both at large μI and small μI
The behavior at large μI is in agreement with the lattice simulation in [6], while the behavior at small μI is different from lattice simulations and previous studies in hard wall AdS/QCD model
Summary
In bottom-up holographic framework, the soft-wall model [40] provides a good start point to describe both chiral symmetry breaking and linear confinement in the vacuum. According to the discussion of [36, 37], with finite isospin chemical potential, the non-vanishing components of scalar field and gauge filed could be set as χ, Π ≡ π1, V03, A10, A20. Where we have imposed the AdS/CFT dictionary and identified the coefficient of the leading terms with quark mass m, chiral condensate σ, pion condensate π1 In this expression, we have neglected the constant term in Π(z) and a2(z), since they are related√to the sources of axial current, which is not be considered in this work. Considering the vacuum value of chiral condensate, the transition temperature of chiral phase transition and the Regge slope of meson spectra, we will follow our previous study and take μ0 = 0.430 GeV, μ1 = 0.830 GeV, μ2 = 0.176 GeV in the following calculation. We will describe the details of numerical results obtained from the soft-wall model given above
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