Emergent gravity on covariant quantum spaces in the IKKT model

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.