Abstract
In this paper, we start with black brane and construct specific space-time which violates hyperscaling. In order to obtain the string solution we apply Null-Melvin-Twist and $KK$-reduction. By using the difference action method we study thermodynamics of system to obtain Hawking-Page phase transition. In order to have hyperscaling violation we need to consider $\theta=\frac{d}{2}.$ In that case the free energy $F$ is always negative and our solution is thermal radiation without a black hole. Therefore we find that there is not any Hawking-Page transition. Also, we discuss the stability of system and all thermodynamical quantities.
Highlights
As is well known, the AdS/CFT correspondence provides an analytic approach to the study of strongly coupled field theory [1,2,3,4]
Using the difference action method, we study the thermodynamics of the system to obtain a Hawking–Page phase transition
The resulting metric may be a solution of field equations with theories with coupling to matter with negative cosmological constant which include an abelian field in the bulk
Summary
The AdS/CFT correspondence provides an analytic approach to the study of strongly coupled field theory [1,2,3,4]. Space-time metrics that transform covariantly under dilatation have recently been reinterpreted as a holography dual to a stress tensor of quantum field theories which violates hyperscaling [5,6,7]. In case of a large scale (or r → ∞), there are good applications of a metric with hyperscaling violation in QCD or string theory. In the AdS/CFT correspondence of finitetemperature, planar black-brane solutions were suggested in the Schrödinger space as the holographic dual of the nonrelativistic conformal field theory at finite temperature. [29] started with a solution of asymptotical black-hole metrics which leads to the string solution This characterizes the specific non-relativistic conformal field theories to which they are dual. While the primary metrics of the two papers are similar, we use the NMT method to obtain a string solution and discuss the phase transition and the thermodynamical stability.
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