A holographic model of deconfinement and chiral symmetry restoration

Abstract

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L x U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1 / 2 \pi R. For quark separations obeying L > L_c = 0.97 * R the chiral symmetry is restored at this temperature, but for L < L_c = 0.97 * R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T = 0.154 / L. All of these phase transitions are of first order.Comment: 30 pages, 7 figures, latex. v2: minor corrections and added reference to parallel wor

Sakai-Sugimoto brane system at high density

“…This is why the χS/χSB phase transition line of the right panel in Figure 11 is terminated at T = T c . When the inter-D8D8 distance L is larger than 0.97R, it has been shown by Aharony et al [37] that the phase represented in Diagram (b) of Figure 10 does not exist. Therefore, the phase diagram becomes rather structureless, as shown in the left panel of Figure 11.…”

“…Horigome and Tanii consider the three known phases, first discovered by Aharony et al [37] at zero density, and the spacetime configurations for the phases are illustrated in Figure 10 the chemical potential, they determined the phase diagram which is schematically shown in Figure 11. 13 The confinement/deconfinement phase transition line at T = T c is determined by the D4-background geometry and the D4 difference action in those phases scales as N 2 c [37]. This is expected to completely dominate the D8 probe actions, which scale as N c N f , so the confinement/deconfinement phase transition line is not affected by the value of the chemical potential.…”

Mesons in gauge/gravity duals

“…6.5 above) at finite temperature. That model also displays a first-order meson melting transition as described in [195,211]. Additional finite density studies can be found in [173,174,[212][213][214][215][216][217].…”

Rho meson condensation at finite isospin chemical potential in a holographic model for QCD

“…At finite temperature it exhibits (at zero chemical potential) three possible phases [24,25]. In the lowtemperature phase, the model is confined and the chiral symmetry is broken to its diagonal subgroup.…”

“…It is derived by considering the decoupling limit of N c D4-branes, compactified on a circle of radius R (x 4 ≡ x 4 + 2πR) with anti-periodic boundary conditions for the fermions [35], intersecting with N f D8-branes at x 4 = 0 and N f anti-D8-branes at x 4 = L. On the field theory side this gives a 4 + 1 dimensional SU(N c ) maximally supersymmetric gauge theory (with a specific UV completion which will not be relevant for us), compactified on a circle with anti-periodic boundary conditions for the adjoint fermions, and coupled to N f left-handed fermions in the fundamental representation of SU(N c ) localized at x 4 = 0, and to N f right-handed fermions in the fundamental representation localized at x 4 = L. In this section we will briefly review the holographic description of this model (see [10,24] for more details).…”