Strings, loops and others: a critical survey of the present approaches to quantum gravity

Abstract

I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity (Regge calculus, dynamical triangulations and simplicial models), Euclidean quantum gravity, perturbative quantum gravity, quantum field theory on curved spacetime, noncommutative geometry, null surfaces, topological quantum field theories and spin foam models. I also briefly review several recent advances in understanding black hole entropy and attempt a critical discussion of our present understanding of quantum spacetime.

arXiv commentPlenary lecture on quantum gravity at the GR15 conference, Pune, India

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Cited by in corpus (26)

• The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
• Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
• (Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
• Black hole scalar charge from a topological horizon integral in Einstein-dilaton-Gauss-Bonnet gravity
• The century of the incomplete revolution: searching for general relativistic quantum field theory
• Loop Quantum Gravity
• Bandlimited Entanglement Harvesting
• Spectral noncommutative geometry and quantization: a simple example
• Self-dual gravity with topological terms
• Nonassociative geometry: Towards discrete structure of spacetime
• Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality
• Relational evolution of the degrees of freedom of generally covariant quantum theories
• Natural Covariant Planck Scale Cutoffs and the Cosmic Microwave Background Spectrum
• Lattice Gravity and Random Surfaces
• Gauge invariance of complex general relativity
• The branch process of the cosmic strings
• Quantum spacetime without observers: ontological clarity and the conceptual foundations of quantum gravity
• The Search for the Origins of M Theory : Loop Quantum Mechanics, Loops/Strings and Bulk/Boundary Dualities
• String Theory and Beyond
• Three mathematical faces of SU(2) - spin networks
• Curving Flat Space-Time by Deformation Quantization?
• Deformations of anti-de Sitter black holes
• Forcing Discretization and Determination in Quantum History Theories
• Five Dimensional Dynamical Triangulations
• Planck Scale Physics, Pregeometry and the Notion of Time
• Discrete spacetime: classical causality,prediction, retrodiction and the mathematical arrow of time