We analyze the thermal phases of a non critical holographic model of QCD. The model is based on a six dimensional background of N c non extremal D4 branes wrapping a spacial circle of radius R and the compactified Euclidean time direction of radius β = 1/T . We place in this background stacks of N f D4 and anti-D4 flavor probe branes with a separation distance L at large radial direction. The analysis of the DBI effective action yields the following phase diagram: At low temperature the system is in a confining phase with broken chiral symmetry. In the high temperature deconfining phase chiral symmetry can be either restored for L > L c = 1.06R or broken for L < L c . All of these phase transitions are of first order. We analyze the spectrum of the low-spin and high-spin mesons. High spin mesons above certain critical angular momentum "melt". We detect (no) drag for ( mesons) quarks moving in hot quark-gluon fluid. The results resemble the structure and properties of the thermal Sakai-Sugimoto model derived in hep-th/0604161.Recently the phases of thermal holographic QCD (HQCD) have been analyzed [1] in the context of the model of Sakai and Sugimoto [2,3]. It was found out that the confinement/deconfinement and chiral symmetry breaking/restoring phase transitions are first order transitions and they do not necessarly coincide with each other. The system may admit an intemediate deconfined phase with broken chiral symmetry.The mesonic world at these phases was later investigated in [4]. The temperature dependence of low-spin as well as high-spin meson masses was shown to exhibit a pattern familiar from the lattice. The Goldstone bosons associated with chiral symmetry breaking were shown to disappear above the chiral symmetry restoration temperature. The dissociation temperature of mesons as a function of their spin was determined, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. It was further shown that unlike quarks, large-spin mesons do not experience drag effects when moving through the quark gluon fluid. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.HQCD models based on critical string theories suffer from the major drawback of incorporating undesired KK modes. Whereas the modes associated with the S 5 in the string theory on AdS 5 × S 5 are essential to describe the dual N = 4 SYM theory, the KK modes in models of HQCD do not correspond to modes of the gauge theory. Moreover, the mass scale of those KK modes is the same as that of the glueballs and hadrons and there is no known method to disentangle the two scales. The most natural way to overcome this problem is to consider strings in non-critical dimensions so as to minimize the set of KK modes. Since the pioneering paper of Polyakov [5]. there have been many attempts to write down an non-critical string model of QCD [6]- [10]. The main problem with non-critical holography is the fact that the corresponding SUGRA backgrounds have curvature of order one and there is no wa...
