Related papers: Quantum Anti-de Sitter Space
We argue that if de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of…
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…
Starting from the classical action for a spin-zero particle in a D-dimensional anti-Sitter (AdS) spacetime, we recover the Breitenlohner-Freedman bound by quantization. For D=4,5,7, and using an Sl(2;K) spinor notation for K=R,C,H, we find…
A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are…
How the spacetime evolved non-perturbatively in a landscape with multiple anti-de Sitter (AdS) vacua, which is theoretically well-motivated, has always been a matter of concern. As a step towards this issue, we perform (3+1)D numerical…
We perform a general analysis of thin-wall Q-balls in AdS space. We provide numeric solutions and highly accurate analytic approximations over much of the parameter space. These analytic solutions show that AdS Q-balls exhibit significant…
Black holes exert quantum pressure coming from the nonlocal gravity correction. We investigate this nonlocal correction for black holes in anti-de Sitter (AdS) spacetime and its dual boundary field theory. We show that the second order…
A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The…
We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…
The supertwistor and bi-supertwistor formulations for ${\mathcal N}$-extended anti-de Sitter (AdS) superspace in four dimensions, ${\rm AdS}^{4|4\mathcal N}$, were derived two years ago in arXiv:2108.03907. In the present paper, we…
The quantization of a scalar field in anti de Sitter spacetime using Poincar\'e coordinates is considered. We find a discrete spectrum that is consistent with a possible mapping between bulk and boundary quantum states.
Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of…
A deSitter brane-world bounding regions of anti-deSitter space has a macroscopic entropy given by one-quarter the area of the observer horizon. A proposed variant of the AdS/CFT correspondence gives a dual description of this cosmology as…
This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum…
We study nonperturbative aspects of quantum field theory (QFT) in rigid anti de Sitter (AdS) spacetime using quantum information theoretic methods. While irreversibility of renormalization group (RG) flows is well established in flat space,…
Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an…
We show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS$_4$) can be described by a minimally coupled scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably…
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…