How General Is Holography?

Abstract

In this thesis I explore the generality of the holographic principle in 2+1 (bulk) dimensions by looking at the possibility of having holographic correspondences for non-AdS (higher-spin) spacetimes. The first part focuses on Lobachevsky spacetimes with $\mathfrak{sl}(4,\mathbb{R})$ as well as ${\mathcal{W}}_N^{(2)}$ symmetries, the asymptotic symmetry algebras and their unitary representations. This results in a family of unitary ${\mathcal{W}}_N^{(2)}$ models that can have both small and large central charge. The focus of the second part is a possible holographic correspondence in asymptotically flat spacetimes. This part covers limits from known AdS${}_3$ results to flat space as well as a NO-GO result that forbids having flat space, higher-spins and unitarity at the same time. In addition this part shows how to consistently add (higher-spin) chemical potentials to flat space. As a non-trivial check of a holographic correspondence in flat space I provide a way to determine entanglement entropy (as well as thermal entropy of flat space cosmologies) holographically in asymptotically flat spacetimes using Wilson lines.

PhD Thesis; Defended on Sept. 7th, 2016; This thesis won the Victor-Franz Hess Prize awarded by the Austrian Physical Society

References in corpus (19)

• Towards a derivation of holographic entanglement entropy
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Entanglement as a Probe of Confinement
• Three-Dimensional Gravity Revisited
• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• A holographic proof of the strong subadditivity of entanglement entropy
• Symmetries of Holographic Minimal Models
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Flat-Space Chiral Gravity
• Notes on the BMS group in three dimensions: I. Induced representations
• Generalized Black Holes in Three-dimensional Spacetime
• Entanglement entropy of black holes and AdS/CFT correspondence
• Lifshitz Holography with Isotropic Scale Invariance
• Holography of 3D Asymptotically Flat Black Holes
• Non-Unitary Holography
• Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge Theories

Cited by in corpus (3)

• Field Theories with Conformal Carrollian Symmetry
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• The nuts and bolts of the BMS Bootstrap