Pion condensation in a soft-wall AdS/QCD model

Abstract

Finite isospin chemical potential µ I and temperature T have been introduced in the framework of soft-wall AdS/QCD model. By self-consistently solve 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. 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 µ I and small µ I . Qualitatively, the behavior at large µ I is in agreement with the lattice simulation in Phys. Rev.D66(2002)034505, while the behavior at small µ I 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 µ I pion condensation phase. This study could provide certain clues to build a more realistic holographic model.

QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model

“…In this paper, we have studied pion condensation and chiral condensation with finite µ I and finite T in the IR improved soft-wall AdS/QCD model. Under a fixed T f , we find that pion condensation exists two critical points separately located in small µ I region and large µ I region, similar behaviors also show in the LQCD in Ref [38], the NJL model in Ref [17] and a solf-wall model in Ref [77]. The behaviors of the pion condensation continuous changes from zero to non-zero and the measured values of critical exponent β are very close to 1/2, which indicates the pion condensation is of second order and belong to 4D mean field class.…”

“…It has been shown that the phase transition, between normal phase and pion condensation phase, is of second-order with mean-field critical exponents and happens at µ c I = m 0 . Efforts have also been made in the soft-wall framework at finite temperature [77]. It shows that the phase transition is of first-order with two both left and right critical µ I at a particular temperature, which are quite different from the hard wall results.…”

“…No explicit source exsits for the axial vector current and a 1 (z) does not appear in other equations, so that we can simply set a 1 (z) = 0 [77]. Equations (12a), (12b), and (12d), are coupled nonlinear second order differential equations with multisingular points, and they do not have exactly analytical solutions.…”

High-energy phase diagrams with charge and isospin axes under heavy-ion collision and stellar conditions

“…The results from these first simulations were in qualitative agreement with the different approaches to QCD . Other interesting approach that is applied to study QCD at finite isospin chemical potential is based in holographic models [62][63][64][65][66][67][68]. More recently, lattice QCD results for finite isospin density were performed using an improved lattice action with staggered fermions at physical quark and pion masses [69][70][71][72], their predictions being in very good agreement with the results obtained from updated chiral perturbation theory [73][74][75] and NJL models [76][77][78].…”

Meson Condensation

“…Given the nonperturbative character of QCD at the energy scales of the various phase transitions in Figure 1, the Lagrangian in Equation (2) is of little direct use. Various theoretical approaches have been developed, including linear sigma models and chiral perturbation theory (χPT) [10,11,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], the Nambu-Jona Lasinio (NJL) models , the quark-meson models [57][58][59][60][61][62], the random matrix model [63,64], the AdS/QCD model [65] and perturbative QCD (pQCD) (with diagrams resummation) [66,67]. A guiding role in this forest of theoretical approaches is played by the lattice QCD (LQCD) simulations [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82], which provide a powerful ...…”