Journal of Holography Applications in Physics
Volume:3 Issue: 2, Spring 2023

In the context of bottom-up holography, we demonstrate the power of mixed boundary conditions to promote the boundary gauge field to be dynamical. We provide two concrete applications of this idea. First, we consider a holographic dual for a strongly coupled plasma described by dissipative magnetohydrodynamics. Second, we reveal the expected features of the Higgs mechanism in a not counterfeit holographic superconductor.

The usual Horndeski black hole do not have $ P-V $ critical points, hence do not show any phase transitions. In this article we a particular modified Horndenski black hole is considered to study the $ P-V $ diagram and the phase transitions. We show that this modified Horndeski black hole solution satisfies the textit{Ist} order phase transition. We also show that the modified Horndeski black hole is holographic dual of a textit{Van der Waals}(VdW) fluid. Finally, we study the thermodynamics of modified Horndeski black hole based on the equation of state originating from the slope of temperature versus entropy. This new prescription provides us a simple and powerful way to study the critical behavior and the phase transition of black holes. The analytical interpretation of possible phase transition points leads us to set some nonphysical range on the horizon radius for the black hole.

The holography principle relates the quantum gravity in the bulk, described by closed string, the gauge theory, described by open string on the boundary with certain asymptotic conditions. Thus, it is important to understand intimate relations between open string theory and closed string theory: In the present work we propose a cubic closed string field theory, introducing a double layer to describe the closed string world-sheet as an extension of the open string world-sheet of the Witten's cubic open string. We mapped the closed string world-sheet onto the complex plane, of which the lower half plane is completely covered by the extended part of the string world-sheet. Using the Green's function on the complex plane, evaluated the Polyakov string path integral, from which we extracted the Neumann functions and the vertex operators.

By applying the holographic method, we study a non-perturbative renormalization group (RG) flow triggered by a gluon condensate. After introducing a bulk scalar field in an AdS space related to the gluon condensate, we investigate the trace anomaly proportional to the gluon condensate. The holographic calculation reproduces the one-loop trace anomaly known in the lattice QCD. We also show that higher loop corrections give rise to additional contributions and modify the one-loop trace anomaly.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

We study hairy black holes in Einstein-Maxwell-complex scalar theory in four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the Robin boundary conditions are imposed on the scalar field. The hairy solutions branch from the Reissner-Nordstr"{o}m-AdS (RNAdS) black holes at the onset of instability of the scalar field under the Robin boundary conditions. There are also associated horizonless solutions called boson stars. Comparing thermal AdS, RNAdS, charged boson stars, and hairy black holes, we obtain phase diagrams in the grand canonical ensemble.