with a background geometry given by $N_c$ D4-branes. They fill four-dimensional Minkowski space-time and extend along a fifth extra dimension $x_4$ compactified on a circle whose circumference is parametrized by the Kaluza-Klein mass. Through this compactified dimension and antisymmetric boundary conditions for fermions supersymmetry is completely broken. Left- and right-handed chiral fermions are introduced by adding $N_f$ D8- and $N_f$ D8-branes which extend in all dimensions except $x_4$. In this compact direction, they are separated by a distance $L\in[0, \pi / M_{KK} ]$. There are two possible background geometries called confined and deconfined phase. For more details about the setup of the model see the original papers by Sakai and Sugimoto, refs. \[18-19\]. In this model, there is a nice topological interpretation of chiral symmetry breaking.

Chiral symmetry breaking is realized in the model as follows. A U($N_f$ ) gauge symmetry on the flavor branes corresponds to a global U($N_f$ ) at the boundary. Therefore, the bulk gauge symmetries on the D8- and D8-branes can be interpreted as left- and right-handed flavor symmetry groups in the dual field theory. The Chern-Simons term accounts for the axial anomaly of QCD, such that one is left with the chiral group $SU (N_f 