arXiv:1105.2872v3 [hep-th] 25 Oct 2011 Preprint typeset in JHEP style - HYPER VERSION Phases of a holographic QCD with gluon condensation at finite Temperature and Density Bogeun Gwak a,b , Minkyoo Kim a,b , Bum-Hoon Lee a,b , Yunseok Seo b and Sang-Jin Sin c a Department of Physics, Sogang University, Seoul 121-742, Korea b Center for Quantum Spacetime, Sogang University, Seoul 121-742, Korea c Department of Physics, Hanyang University, Seoul 133-791, Korea Email: rasenis@sogang.ac.kr, mkim80@sogang.ac.kr, bhl@sogang.ac.kr, yseo@sogang.ac.kr, sjs@hanyang.ac.kr Abstract: We study the phase diagram of a holographic QCD using the probe D7 brane in the black D3 geometry with the finite D-instanton charge. Due to the quasi-confining nature of the geometry, a baryon vertex can exist outside the horizon so that we can find D7 brane embeddings with the finite baryon density and the finite chiral condensation as well as an embedding where only quarks are possible but the chiral condensation can be zero or non-zero. We study the phase transition and the phase diagram between these phases. We also calculated the constituent quark mass and the binding energy of baryons as function of the density. Keywords: Gauge/gravity duality, Dense matter, Finite temperature gauge theory, Phase transition.