Emergent gravity on covariant quantum spaces in the IKKT model

Understand

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.