Abstract
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over S 4, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.
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Steinacker, H.C. Emergent gravity on covariant quantum spaces in the IKKT model. J. High Energ. Phys. 2016, 156 (2016). https://doi.org/10.1007/JHEP12(2016)156
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DOI: https://doi.org/10.1007/JHEP12(2016)156