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.
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Steinacker, H.C. Higher-spin gravity and torsion on quantized space-time in matrix models. J. High Energ. Phys. 2020, 111 (2020). https://doi.org/10.1007/JHEP04(2020)111
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DOI: https://doi.org/10.1007/JHEP04(2020)111