On the quantum structure of space-time, gravity, and higher spin in matrix models

Abstract

In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by Yang-Mills matrix models, which allow to consider space-time as a physical system, which is treated on the same footing as the fields that live on it. We discuss a specific quantum space-time solution, whose internal structure leads to a consistent and ghost-free higher-spin gauge theory. The spin 2 modes give rise to metric perturbations, which include the standard gravitons as well as the linearized Schwarzschild solution.

32 pages, 2 figures. V2: references added, minor corrections. V3: improved presentation, published version

References in corpus (3)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Toeplitz operators on symplectic manifolds
• Higher-spin gravity and torsion on quantized space-time in matrix models

Cited by in corpus (18)

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• One-loop effective action of the IKKT model for cosmological backgrounds
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• String modes, propagators and loops on fuzzy spaces
• Infinite distances in multicritical CFTs and higher-spin holography
• Gauging the higher-spin-like symmetries by the Moyal product
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
• The fuzzy BTZ
• Spatially flat cosmological quantum spacetimes
• Quantisation of type IIB superstring theory and the matrix model
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
• Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem