Higher-spin gravity and torsion on quantized space-time in matrix models

Abstract

A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy-momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metric and torsion transform covariantly under a higher-spin generalization of volume-preserving diffeomorphisms, which arises from the gauge invariance of the matrix model.

arXiv comment37 pages, 1 figure. V2: improved discussion, published version. V3: minor corrections

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• A Twistorial Description of the IKKT-Matrix Model
• Fermions on curved backgrounds of matrix models
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• One-loop effective action of the IKKT model for cosmological backgrounds
• Gauging the higher-spin-like symmetries by the Moyal product
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Fuzzy Schwarzschild (2+1)-spacetime
• Quantisation of type IIB superstring theory and the matrix model
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
• Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection
• Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes