Therefore, the various gauge and gravitational anomalies, which arise as one-loop effects, cancel and as we expected theory is perturbatively well-behaved \[79-82\].

In this section, we study a model which is similar in many aspects to the SS model \[18\], a holographic model based on the critical string theory. But, we try to solve some inconsistencies of the SS model in describing the baryons via the non-critical $AdS_6$ model.

$AdS_6$ model
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In the presented non-critical model, the gravity background is generated by near-extremal $D4$ branes wrapped over a circle with the anti-periodic boundary conditions. Two stacks of flavor branes, namely $D4$ branes and anti-$D4$ branes, are added to this geometry and are called flavor probe branes. The color branes extend along the directions $t,x_1,x_2,x_3,$ and $\tau$ while the probe flavor branes fill the whole Minkowski space and stretch along the radius $U$ which is extended to infinity. The strings attaching a color D4-brane to a flavor brane transform as quarks, while strings hanging between a color $D4$ and a flavor $\overline{D4}$ transform as anti-quarks. The chiral symmetry breaking is achieved by a reconnection of the brane, anti-brane pairs. Under the quenched approximation $(N_c \gg N_f)$, the reactions of flavor 