Related papers: Flow equation, conformal symmetry and AdS geometry
We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We…
We study the proposal that a $d+1$ dimensional induced metric is constructed from a $d$ dimensional field theory using gradient flow. Applying the idea to the O($N$) $\varphi^4$ model and normalizing the flow field, we have shown in the…
We show that the anti-de Sitter(AdS) space naturally emerges from the conformal field theory(CFT). The behavior of the leading divergent term in the entanglement entropy implies the underlying AdS geometry. The coefficient of the leading…
We propose a method to define a $d+1$ dimensional geometry from a $d$ dimensional quantum field theory in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation,…
We show that quantum dynamics of any systems with $SU(1,1)$ symmetry give rise to emergent Anti-de Sitter spacetimes in 2+1 dimensions (AdS$_{2+1}$). Using the continuous circuit depth, a quantum evolution is mapped to a trajectory in…
A quantum field theory on Anti-de-Sitter space can be constructed from a conformal field theory on its boundary Minkowski space by an inversion of the holographic mapping. To do this the conformal field theory must satisfy certain…
Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional…
We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that…
We propose a method to give a $d+1$ geometry from a $d$ dimensional quantum field theory in the large N expansion. We first construct a $d+1$ dimensional field from the $d$ dimensional one using the gradient flow equation, whose flow time…
The standard geometric description of $d$-dimensional anti-de Sitter (AdS) space is a quadric in ${\mathbb R}^{d-1,2}$ defined by $(X^0)^2 - (X^1)^2 - \dots - (X^{d-1})^2 + (X^d)^2 = \ell^2 = \text{const}$. In this paper we provide a…
This work is intended to investigate the geometry of anti-de Sitter spacetime (AdS), from the point of view of the Laplacian Comparison Theorem (LCT), and to give another description of the hyperbolical embedding standard formalism of the…
By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a…
We consider the AdS/dS CFT correspondence and study the nature of the thermal bath of the de Sitter field theory using holography. Unlike the temperature of a thermal field theory in flat spacetime, the temperature of a superconformal field…
Massive fields on anti-de Sitter (AdS) space enjoy galileon-like shift symmetries at particular values of their masses. We explore how these shift symmetries are realized through the boundary conformal field theory (CFT), at the level of…
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic…
In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant $\Lambda$ and a 4D de Sitter (dS) space. In this paper we present…
In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski spacetime in d-dimensions. The curvature dependence appears in a very simple way through a…
We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in terms of those in d dimensional anti-de Sitter space. The procedure, which is neither dimensional reduction nor dimensional compactification, is called dimensional…
The ambient space of dimension d+2 allows to formulate both fields on AdS(d+1) and conformal fields in d dimensions such that the symmetry algebra o(d,2) is realized linearly. We elaborate an ambient approach to the boundary analysis of…
We present a framework for generative machine learning that leverages the holographic principle of quantum gravity, or to be more precise its manifestation as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, with…