  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.
