^{3}.

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 into the confinement/deconfinement transition. The plots of grand potential versus temperature and chemical potential versus transition temperature are obtained.

Strongly interacting systems are always a challenge to our analytical knowledge. Quantum chromodynamics is such a theory, which cannot be solved analytically in low energy regime. There are two methods to solve QCD; one is “lattice QCD” [

There are two approaches from where one can construct QCD like theories. These approaches are known as top-down and bottom-up approaches. In top-down approach, one starts from stringy D brane configurations and constructs models for QCD [

The transition between confining and deconfining phase is studied by Hawking-Page transition in bulk spacetime [

In the charged black hole solutions, charge of black hole is related to chemical potential of the quarks. The dual gauge theory defining the deconfining phase is AdS black hole while the confining phase is defined by thermally charged AdS solutions [

The study of gauge/gravity duality provides a relation between the gravity theories in the AdS spacetime and conformal field theories on the boundary of the AdS spacetime. In recent years, a large number of generalized geometries are studied, which gives a dual scale invariant gauge theory. One of the metrics representing such a geometry is given by

In this paper, we study the effect of warping on confinement/deconfinement transition in the simplest case by taking the value of

This paper is organized in six sections. In Section

In this section the solution Einstein-Maxwell-Dilaton system with hyperscaling violation [

The equations of motion for gravitational part of action (

Let us consider the ansatz for our metric (with

Using our ansatz, the solution for Maxwell’s equations can be written as

On solving

Using equations of motion, the metric function is given by

In this section, we consider the black hole solution for the warped geometry. The solution of

Using equation of motion, action (

The above action is singular at

This section is devoted to the study of thermally charged AdS solution [

The field strength tensor for thermally charged AdS is given by the same equation as that for AdS black hole case, but now

Using the same procedure as done for AdS black hole, we compute regularized action for thermally charged AdS, which is written as

Now we study the transition from AdS black hole phase to thermally charged AdS. To study this, we take the difference between the actions of AdS black hole and thermally charged AdS geometries with appropriate periodicity matching. The difference in grand potentials is proportional to difference in actions. The difference in actions is given by

Grand potential versus temperature at various values of

For

For

The relation describing the five-dimensional gravitational constant and that of the five-dimensional gauge coupling constant are evaluated by the application of AdS/CFT to QCD. These constants relates the colour gauge group (

The value of

In this paper, we studied the thermodynamic behavior of AdS/QCD from holographic approach with generalized warp factor. The plots of grand potential per unit volume are shown in Figure

Figure

The author declares that there is no conflict of interests regarding the publication of this paper.

S. Sachan is supported by CSIR-Senior Research Fellowship, Grant no. (09/013(0239)/2009-EMR-I). The author would also like to thank Dr. Sanjay Siwach for discussing the problem at various stages of this work.