Related papers: Kinematic space and the orbit method
Kinematic space can be used as an intermediate step in the AdS/CFT dictionary and lends itself naturally to the description of diffeomorphism invariant quantities. From the bulk it has been defined as the space of boundary anchored…
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is…
This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant K\"ahlerian structure. These…
The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic…
We consider the computation of volumes contained in a spatial slice of AdS$_3$ in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or…
We obtain a Principal Kinematic Formula and a Crofton Formula for surface area measures of convex bodies, both involving linear operators on the vector space of signed measures on the unit sphere $S^{d-1}$. These formulas are related to a…
We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First we display a nonlocal map that commutes with the de Sitter isometries, transforms the bulk-boundary…
This paper investigates the entanglement entropy inequality and explores the presentation of mutual information and conditional mutual information in kinematic space. Specifically, we examine the regions within kinematic space responsible…
Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a spacelike…
The present article presents geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjoint orbit of an infinite-dimensional Lie group constructed…
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…
According to Ryu and Takayanagi, the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We study this holographic geometrical method of…
We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…
We study the construction of a manifestly covariant worldline action from a coadjoint orbit. A coadjoint orbit is a submanifold in the dual vector space of a Lie algebra, generated by coadjoint actions. Since a coadjoint orbit is a…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
In this thesis, we aim to understand the microscopic details and origin of the Cosmological Horizon, produced by a static observer in four-dimensional de Sitter (dS$_4$) spacetime. We consider a deformed extension of dS spacetime by means…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…
For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the…
We write down Crofton formulas--expressions that compute lengths of spacelike curves in asymptotically AdS$_3$ geometries as integrals over kinematic space--which apply when the curve and/or the background spacetime is time-dependent.…
We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive,…