A holographic model of deconfinement and chiral symmetry restoration

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)symmetry is restored at this temperature, but for left-handed quarks and N-f right-handed quarks which are localized at different points on the 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 similar or equal to 0.97 * R the chiral L < L-c similar or equal to 0.97 * R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T chi(SB) similar or equal to 0.154/L. All of these phase transitions are of first order.