We study the thermodynamics of soft wall model in AdS/QCD framework. The low temperature phase of QCD is described by thermal AdS and high temperature phase by AdS Black hole solution of five dimensional gravity with negative cosmological constant. The chemical potential is introduced via the solution of U(1) vector field in the bulk. The difference of action densities in two phases is studied and the results are compared with hard wall model. The quark number susceptibility is also calculated in both the models.

The entanglement entropy correlates two quantum sub-systems which are the part of the larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in (2 + 1) dimension by applying numerical techniques to entanglement entropy approach. This (2+1) dimensional massive theory can be obtained from (3+1) dimensional massless scalar field via dimensional reduction. We also calculated mass corrections to entanglement entropy for scalar field. Finally, we observe that the area law contribution to the entanglement entropy is not affected by this mass term and the universal quantities depends upon the basic properties of the system.

We study analytical solutions of charged black holes and thermally charged AdS with generalized warped factors in Einstein-Maxwell-Dilaton system. We calculate Euclidean action for charged AdS and thermally charged AdS. The actions in both backgrounds are regularized by the method of background subtraction. The study of phase transition between charged black hole and thermally charged AdS gives an insight to the confinement/deconfinement transition. The plots of grand potential vs temperature and chemical potential vs transition temperature are obtained.

The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is the modification of the Schwarzschild black hole. We present the Bardeen black hole solution in presence of the dRGT massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution interpolates with the Bardeen black hole in the absence of massive gravity parameter and the Schwarzschild black hole in the limit of magnetic charge g=0. We investigate the thermodynamical quantities viz. mass (M), temperature (T), entropy (S) and free energy (F) in terms of horizon radius for both canonical and grand canonical ensembles. We check the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity flips the sign at r = r_c. The black hole is thermodynamically stable with positive heat capacity C>0 for i.e., globally preferred with negative free energy F < 0. In addition, we also study the phase structure of the obtained solution in both ensembles.

We investigate the thermodynamics of confinement/deconfinement transition in soft wall model of QCD with Gauss-Bonnet corrections using AdS/CFT correspondence. In bulk AdS space-time the transition is geometric and is known as Hawking-Page transition. The Hawking-Page transition between two geometries, namely charged AdS black hole and thermally charged AdS have been studied with Gauss-Bonnet corrections up-to first order. The Gauss-Bonnet coupling modifies the transition temperature of the system, but qualitative features remain unchanged. We obtain the curves between chemical potential and transition temperature for different values of Gauss-Bonnet couplings. We find that there exist a point in μ-T plane where lines with different value of Gauss-Bonnet coupling cross each other. This point may be the onset of the transition from first order to cross over behavior. The results are compared with that of the hard wall model.