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 × 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 = 1/2π 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 χSB ≃ 0.154/ L. All of these phase transitions are of first order.