show that the results of these models for some low energy QCD properties such as the meson mass spectrum, Wilson loop, and the mass spectrum of glueballs \[45-47\] are comparable with lattice computations. Therefore non-critical holographic models still seem useful to study QCD.

One of the non-critical holographic models is composed of a $D4$ and anti $D4$ brane in six-dimensional non-critical string theory \[43,45\]. The low energy effective theory on the intersecting brane configuration is a four-dimensional QCD-like effective theory with the global chiral symmetry $U(N_f)_L \times U(N_f)_R$. In this brane configuration, the six-dimensional gravity background is the near horizon geometry of the color $D4$ branes. This model is based on the compactified $AdS_6$ space-time with constant dilaton. So the model does not suffer from large string coupling as the SS model. The meson spectrum \[45\] and the structure of thermal phase \[48\] are studied in this model. Some properties, like the dependence of the meson masses on the stringy mass of the quarks and the excitation number are different from the critical holographic models such as the SS model.

We study the gauge field and its mode expansion in this non-critical holography model and obtain the effective pion action 