quenched gluodynamical background, where the flavor dynamics is added as a probe.

The remainder of the paper is organized as follows: We give a review on the quenched dynamical holographic QCD model in Sec.\[sec-action\]. In Sec.\[deconfinement\], we fix the chemical potential dependence of the dilaton potential which describes gluodynamics through the baryon number susceptibilities and investigate the deconfinement phase transition in the $(T,\mu)$ plane. In Sec.\[chiral\] we investigate the chiral phase transition and the phase diagram in the quenched dynamical holographic QCD model. In Sec.\[sec-sum\], a brief summary is given.

Setup for the quenched dynamical holographic QCD model at finite baryon chemical potential {#sec-action}
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The deconfinement phase transition has been widely investigated in bottom-up holographic models [@Herzog:2006ra; @BallonBayona:2007vp; @Cai:2007zw; @Cai:2012eh; @Kim:2007em; @Andreev:2009zk; @Colangelo:2010pe; @Gubser:2008yx; @Gubser:2008ny; @Gubser:2008sz; @Gursoy:2008bu; @Gursoy:2007cb; @Gursoy:2007er; @Gursoy:2008za; @Yaresko:2013tia; @Li:2011hp; @Cai:2012xh; @He:2013qq; @Yang:2014bqa; @Zuo:2014iza; @Afonin:2014jha]. Besides, it is possible to describe the chiral symmetry breaking and its restoration in the soft-wall model [@Karch:2006pv; @Chelabi:2015cwn; @Chelabi:2015gpc]. In this work, we investigate the interplay between the chiral and deconfinement phase transitions by using the dynamical holographic QCD model [@Li:2012ay; @Li:2013oda; @Chen:2015zhh; @Li:2014dsa; @Li:2013xpa; @Li:2014txa]. We emphasize that though the original AdS/CFT correspondence is in the large $N_c$ limit, the 