Journal of Holography Applications in Physics
Volume:4 Issue: 1, Winter 2024

One of the major developments in classical black hole thermodynamics is the inclusion of vacuum energy in the form of thermodynamic pressure. Known as Black Hole Chemistry, this subdiscipline has led to the realization that anti de Sitter black holes exhibit a broad variety of phase transitions that are essentially the same as those observed in chemical systems. Since the pressure is given in terms of a negative cosmological constant (which parametrizes the vacuum energy), the holographic interpretation of Black Hole Chemistry has remained unclear. In the last few years there has been considerable progress in developing an exact dictionary between the bulk laws of Black Hole Chemistry and the laws of the dual Conformal Field Theory (CFT). Holographic Black Hole Chemistry is now becoming an established subfield, with a full thermodynamic bulk/boundary correspondence, and an emergent understanding of CFT phase behaviour and its correspondence in the bulk. Here I review these developments, highlighting key advances and briefly discussing future prospects for further research.

We present a version of holographic correspondence where bulk solutions with sources localized on the holographic screen are the key objects of interest, and not bulk solutions defined by their boundary values on the screen. We can use this to calculate semi-classical holographic correlators in fairly general spacetimes, including flat space with timelike screens. We find that our approach reduces to the standard Dirichlet-like approach, when restricted to the boundary of AdS. But in more general settings, the analytic continuation of the Dirichlet Green function does not lead to a Feynman propagator in the bulk. Our prescription avoids this problem. Furthermore, in Lorentzian signature we find an additional homogeneous mode. This is a natural proxy for the AdS normalizable mode and allows us to do bulk reconstruction. We also find that the extrapolate and differential dictionaries match. Perturbatively adding bulk interactions to these discussions is straightforward. We conclude by elevating some of these ideas into a general philosophy about mechanics and field theory. We argue that localizing sources on suitable submanifolds can be an instructive alternative formalism to treating these submanifolds as boundaries.

Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories, making it a good starting point for investigating the origin of non-trivial vacua. The adaptive perturbation method is a technique used to handle strongly coupled systems. The study of strongly correlated systems is useful in testing holography. It has been successful in strongly coupled QM and is being generalized to scalar field theory to analyze the system in the strong-coupling regime. The unperturbed Hamiltonian does not commute with the usual number operator. However, the quantized scalar field admits a plane-wave expansion when acting on the vacuum. While quantizing the scalar field theory, the field can be expanded into plane-wave modes, making the calculations more tractable. However, the Lorentz symmetry, which describes how physical laws remain the same under certain spacetime transformations, might not be manifest in this approach. The proposed elegant resummation of Feynman diagrams aims to restore the Lorentz symmetry in the calculations. The results obtained using this method are compared with numerical solutions for specific values of the coupling constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for quantum triviality, where self-consistency of the theory in the UV requires $\lambda = 0$. This result implies that the $\phi^4$ theory alone does not experience SSB, and the $\langle \phi\rangle = 0$ phase is protected under the RG-flow by a boundary of Gaussian fixed-points.

In this article, we present a heuristic derivation of the on-shell equation of the Lorentzian classicalized holographic tensor network in the presence of a non-zero mass in the bulk spacetime. This derivation of the on-shell equation is based on two physical assumptions. First, the Lorentzian bulk theory is in the ground state. Second, the law of Lorentzian holographic gravity is identified with the time--energy uncertainty principle. The arguments in this derivation could lead to a novel picture of Lorentzian gravity as a quantum mechanical time uncertainty based on the holographic principle and classicalization.

This study investigates the non-equilibrium dynamics of massive N=2 supersymmetric gauge theory under pulse-like electric field quenches, utilizing holographic techniques within the AdS/CFT correspondence framework. Focusing on subcritical electric fields, our analysis reveals prolonged oscillations in the electric current as well as the quark condensate dynamics with no dissipation. Notably, through power spectrum analysis of the time-dependent electric current, we identify a dominant frequency in the oscillations, which remains the same within numerical precision across different parameter variations, serving as a universal feature of the system.

In this paper, we consider a metric of a rotating black hole in conformal gravity. We calculate the thermodynamical quantities for this rotating black hole including Hawking temperature and entropy in four-dimensional space-time, as we obtain the effective value of Komar angular momentum. The result is valid on the event horizon of the black hole and at any radial distance out of it. Also, we verify that the first law of thermodynamics will be held for this type of black hole.