in Fig.\[chi\]. It is found that when $h(\Phi) = \frac{7}{10}$, the result of kurtosis from the dilaton background, i.e., from the gluodynamical contribution in the quenched dynamical holographic QCD model is in good agreement with lattice results.

![$\kappa\sigma^2$ as functions of the normalized temperature $T/T_0$ with $T_0=217~{\rm MeV}$ the pseudo critical temperature at zero chemical potential $\mu=0$. The black line is for $h(\Phi)=7/10$ which is in agreement with lattice results in Ref.[@Bazavov2017The]. []{data-label="chi"}](chi.eps){width="6.5cm" height="4.5cm"}

With the setup in this section, we are ready to investigate the deconfinement and chiral phase transitions in the quenched dynamical holographic QCD model at finite temperature as well as finite chemical potential.

Deconfinement transition at finite baryon density {#deconfinement}
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In order to investigate the deconfinement phase transition, the expectation value of the Polyakov loop is often used as an order parameter, which is defined as $$\begin{aligned}
L(T) = \frac{1}{N_c}{\rm Tr}{\rm P}~ exp(ig\int_{0}^{\frac{1}{T}}\hat{A_0}(\tau,\vec{x})\,d\tau).\end{aligned}$$ Here $N_c$ is the color number, P indicates path ordering, g is the coupling, the trace ${\rm Tr}$ is computed over the fundamental representation of $SU(N_c)$ and $\hat{A_0}$ is the non-Abelian gauge field potential operator. The expectation value $\langle L(T)\rangle$ vanishes in the confined phase guaranteed by the center symmetry, and it 